LIBRARY OF CONGRESS. 



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UNITED STATES OF Alfefiroi. 



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OF EHQlNEEfJNiQ ly JrvinfT. Ckufvh.C.t 



C omell ■ LLnioer Ttly , ItWca, M . Y. 



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Tabu or cc^ntent^ . ^ 

CHAP I. E;lsineniarv/ S^^cbSs'i anA Stlra.w>S ,..^3. I 

^^ COMpf^^SSic?^^ op SHORT 13lorKS . ..,.,, ^.i?&' 

^ Q.C2 . llern^HS <?k, crw'sWn^, 

"^ ?iO^\ factor 4 IraffrTv '^.C^g frswiiial Tvrft<S 

^Sk£AF?lN5 . - - . p.?6 

§ 2o7, ^\y<h ^&6 5Weatn>«Wt*Lnrrion t^^?. Skt&vfv*^ stress «») • 
^*.v* «{ tbe Same HTWjr^y en iVie f««r-fe« «^ ot^^i^cnf. 

CUAP, XL. TorsiO^. _ . >,S1 

^ lib Tcr'i>kjncA S^rUn^jtVi, 5.\'?, Toy*. sVffnesS, ^li'" tfi^. Wi^»ew*<. 
^ *XVj *f^o\aT moment <j( in<^«<i . :2^0, >iow- cIrcJUr '^Koift^. 

CHAP. m. Fl€XHt€ a[ Komdj. j>»i4ms Un^ 
^!l^fe TV»e ^^^.Sfic jorceS. ^"^.7.Ncu.WqL>tW C0n\am5 centre rf( <p«v%Ii^ 

^ 2^3. Kor,a»nLi\ Uffl|,«^^5 ^c^jj^-rJU ,Vul ^. mi,^« . ^'^^.liUU, 



TABi.? cf CONTENTS 



>. Iti- 



BQ*^6, fl<7r("2Cr^t beanr», «vv<ii St-tjipoyiedijlOGui ujn{{crM <?V€V w!-vaI<L l^^Tk 
^ '''^'7 Cc^nlilevfer^ ^ 23S, K<rri-2.,lD<«in^ , e.<?u.ciil UrmiVioJ loads. 
SAF& XOAPS INT FlEXVifeE 

^ 2 ^ /. H cmz^'tvectivVy ertji s Su.j>porfei^ central IcacL 5^ ^. D !tic "but > #W- 

^^^"I 1^ etc .^jo vavWs tvvaterv«ls %^7, Wuu*Tor\ca) £xa»wp^^S 

5^:^57 Rw^tln-w joy D^i)t beorrtS 

*S ilS'ir,!De5i^Tir^^ secT/ovtS ^ built "bcoHms, 55^ Set df nx^vta*; teaiis 
^260 S\r^<^W ccceM>cC loouJ ^6\ Two e4*«»* fen^rn*^ ii«»4^ 
i ^6il loo^ w.tti!(orTvi rverVkAYl df S^«t> • Zi3 D>Ud ov«y vAoW^i^n. 

^ X(^C> .Four cWnvoTiv/^s ol^iosnc ^v^rvA, 2$7. t^eSia'e^it^ ^ WAwt. 

CHAR IVCFUx-^^ C^nlmu.ciy^^'^^^^'^^^^^ Cl ><J^ii/?fi 

^^ 27 1 P-rfirivtwn . ^7^.*Tvv<s e<?w.al sjx^vts^ eev^lrol Ic^s. 

5 '-^73 "tDido • CA\'\^^C>■Tv^ )oa4'» OV^T- vvV)cltf S^»tS, Q.lh PrT^»^*Iji:o«a*^^ 

KCK-p1?!S)vcATiC. e FA IV)S OF "OVIFORM ST l^PKCrfT 



TASLE OF coNTG-N-TS > iv. 



§ ^^V Remarks. S^S' possi^vc^^ou <si tk^ eWsttc force-S . 

% ^96* <i, ELccSUc curr^. -2^6 C'bl^u^ caruv Wey v/i^ Ferinii^' )oci«J . 

§^^f .Nru.m«n'ccil ^oiJv^jVu 3^0 Hooks, 30l Crane. 
CV.oii.Tr, Fiexixxt crf^Xonq CoUm^iS " |>J3^ 

§350 Built ColixmtiS, Sll Mom^nf^ <?{ m«rlia c{ buili CMuuriv^^. 

C k(5ij?.l7ir . L mear Cl^$ (#f bUxWtrrk;) , v,, 1S6 

§.3)6. B).<K:i^weTr)< arch, 3^6 . i.*i<«>- «anrcU«5 . 
*3 3i'^« Xr:>#^Trft4 colevvoary. 3t^, Xir^co^' orcW^ unirf ^TV-ew. loAiL^ 
% Sl'^^C^rcJlav ore a4 Vm eov -oreff , S3.0 ^txrahcla AS linear- atck."^ 
% 351. 1vl"<Wr ccrck^arcjtvCM uy>f>-€3ft»%L*«- 4ff UcuJ ^^..^^ I3J63 

5 33 11. ^pf^ ttfvito^y ^ -dioj^ V»e^ 3tl3 J?emarUi, 

% 33*^. TW S^pet^oi H«^uii. ?o"\A/<^ot> 'VU reUiialb \He Presses m \t»e 
ixt^a rv>e,f FORCE DIAGRAMS V. ., . ■^. flS6. 



TABXE (^F CONTENTS ^.^ 



% 2>5'C. TVie tWelii^ear arc}\ S6 ) 2x.^t«l<£5H of the S«trrt€. 
^ 36'^. pTtxchc^l Ci7n elusions. 

ARRANGE MH?^T<5Fl>ATA f<3R GicApiW: TRFATN>i?w-r^.^u 

^ 3v^7 P»€ys oin^ oi)vtT^-ey>t , 

(GRAPHIC T]^£AtK)HN^T of ARCH ,_ ^^ -j^.^c^ 

ci^-^ u.4fi^\jv>\rv»<rY»'ca] ii?caitn«. 3^0, C cyt<i/L'<cfvt5 o] Safe <5e*s*^*i. 








^ ?>76, Su.mvKt.Alii>vt «■[ |>TO<^u.cfe 37^. QravAy veVt^Ca.\ 

% 377. Con^\y<x^Uon jcr 1W Vtn U n^A^e ^ <C «= *iw^, J Xtv^ 

^ ^^S' " - '^ ; fixed ev^As ^^'i 

S 3%7. Re-^ai-ne , ^ 

>{of?\Z(DMrAX. STRAIGHT ClRPHRS^-)>.'^V« 



Fi5S. 1^2 foiiOO,To^acey 



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Mcrm rr. 




\F«V. I*?? § /82 
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^AF Fig. i'J? ^ l^/ . 



Rg. 500 § \n 




PART n 

StKEKSJTM Of iV(ATERlAls. 

Cliap. Lolcmeutqy Stresses & Strains. 

l78.T>EfOpMAt!OK^ Cf S0).lDjBoDlfcS. In -Hie 
brece4»a6' WTHons 6\ l^u's vvcr'^ , W^ul w^S called techmcallvcL 
•Viijid b*i'iy'\va.s. suj»)>^5ed vncab^^Ae o] «iha\icj\n^ its -(orm^J.e. Hie 
"bcsclWns <( i^^ patTiclei yelaSiufelv ^^ «^^^ chcr^under he. ort»cn of 
Any foY<ieS lo be Vc;uiflit L^pcn it . \ b«S sitj^poSilTon wc^s made W 
cauS€ ffce Ciian^e of |or\^^ wK«c1a rnusX artua'i^y <JCcu.r does ^ not 

Uire ov ^TLO^VuVte, Id sU^^v^ Itov^ tlie. jri^tvi'dual bieces ^ suck 
corisJ-rucHo^is sWouL^ be dssi^^i^ec^ u awo'icl undeslraljle deform a- 

As )3«Tl7a.t)S Hie SunJslesV in ^Fawtre ©I the dejormaRon ey 4is- 
[irUiJu s( a 5o1icl^lA uS ccnsic^ev the case <5^[' a brismadc rod. 

in a state o"| te*^.S(i?f\ j Tiu , l^.? Tlink of a Suvvsj/ors cKam^ 
€.^.\ \he jauU ci eacli ei^d. l& ^^ana die to3]; )& s*^^ To W w*i- 

dev a. "tension tfj X Q''^., ^»tS^ or ctkcr umU^ loot ^X* 
Lei ABCT) be 1he eiici vjcw o'[ an eleinei-^^avy l^arcOlelobibc^^ 
ori'^inally of Square Sectioa ^^"^^ vjU\i -faces qt 45^wirh [tie 
ax\S Oj tl^C |)r«'sm. Jii is now <Aejorme<i^tKe 'jou.^ faces bcr- 
jbew.dccu.lAV' to V\t ha^ey teivi4 Uw^ev tl'taa Wfdre^ wkje itxe <?k- 
olcs ^AD a>ai5 BCD oTMirialW ricjlit an^^U^^ are now -shr>a1lev 
^ H cer\a.i¥K. amount £ ^ ABC and A^C Xar^ey V>y cut €<3«.cal 
amoaht 0. 1 .nd elemeot is sai<d to log ma stafe of SJRAI'Y^ 
Viz.: tke eloin^oTioa <?{ ifs edi^es (j)ey[>eiAdKu'cii^ u» ha^JCK*) Is 
calUd a TEWS^Lt STl?AlM,wkilc tlie olfevciTiJh mlWcq- 



tl78 ELE^4, STR ESSES^ etc, 



oUs ]pi:!wfecn ll'S faces i& caUe<i tx b\i£a'r;r O sTratr i or aia<^«^- 

since BC Vv'^-s \>eer> WKxde !o s\k^c^ re'\<aljv/£ly t© AO^andLlluye^' 
caused l\\e cWv^^e of <:vr\<:;je). | 1 H<s «^*»« o'[ tt^e word sTrw,*^^ 
1o si^ni'^Y cKaUi^e ot ^crm ^h.d udt TKe force J)Tt3ciu.<(i-ic it ^ is cf 
recent ado^jtou oimono nu^v^lhou^K nbt ca]l ,l2:clvfcal vvriTfersri 
17?. ^T»^Al^/S. Tvvo'KJN'PS O.Nky, Just a.s o, .jiv- 

64^ Vine tn<>ky t^ co»^Sidcrrecl to 1??: i^oAe, ^ ^ S\na\\ slvcu,^ut !i«t" 
cWdisWTs ic> the scfcla^lcuice ^5 otum Soi«*i l^ody ma.y i^e constdeKd 

are e«<:K "^i*^** Wfcrre tV<£ \>cciy is S*Aje.c!»2ci fe TKs ^x-cHon of farces 
"buC vuKick o' e not ^ecfs^ianly cubes. A luie* ^ iucU e\ct\tsn(5 

IKiS «ioe3 net r\ec£S5rdin\y vr.^ply ap'^^'*^"'^ naluire- irt Rte mcdsr^i- 
o\ tn ^^^^sTfOix, I n«i ^yskiw ©j irT>a.<::^ii'>avy <«^tivty sur][ac€S W 

vJhicK ^-x^ \3c^y W \\\mS Suj^diVidecl nc«4 laot Consist cnRrely of 
|>latie5 '5 m the. suo^Vt of Ic^rsion, |or msTcwice^Hte "jpara)lelo))>j>a<. 
icai eletnent$ co^\s'uiere<^ V© m cotr^reiA $y«c t^hn civic 0.1 sheDs^cut 
"kolli \y trci^svcYse <xv^<ii radial T?lan<ts. 

p\t\ce these e\eir»enls ar-e Ictkew so ♦JiwaU tltat tlie cnly hos- 
%ibie clwyvrjesof "jorni m a1^y out ftf iii«ti'\j AS in<luc«<l Is^ <x. 5y5- 
l<rtn ef fixfetna.! T«js~c«5 atflmy <?!> i^^e 'h^dy are ftl<3w^«^t?«i5 «>- 
contvorcUoMS 6[ ills ed^s^avt^ «iliet«:dto5t <jf \U cHn<i|Uii^ ftesrc c<r< 
tut Iwo kiviiis ftf sWm EjLO)^'{3ATiOA/^ (^ conlYtx-cRoit If^e^. 

180. DlSrRiBUri^P fOKCS^^or%XH2SS^S)An 

Ifca] "bu.r}>o3«s Te? coi^Cidt)r a f ovcc fi<.s aj>]>ij'e(i at ^ 'bomt of 
a IffOiiy^Vut ir\ ycc^lity "{t xryust ^^ SisXriiu^ed. ovcr a. definiTe a- 
>«CL; for 0l\r\€YW\S^ n^e mc^f^i-ial WouU JaC. ^uiyj^cTed lo c<«a 
xirifinire force )>er unit <»f Or^O-, /^ FoKCS like <^rav%ly ^ v>u?ifi'- 
^l^»s alTyucUoii elc. w€- 1t<;^v£ oilv-«a<k Weafed as dtstn/^ui^ct 
<s>v€r tke rwo-ss <5f m. ^^iy, ^ut refe^^kvie \s ri<>v/ Kcu^ |)arrc- 
uiarly to tke ]3rc$suve of cm^ "l5d<i^ o^^iust ai^ol^^ft-^ or 



%e. (xtXion 6\ on? jporlToi-i oj %6 hody ot\ the rciv^aiocier.j for 
\v.s\c\act^ sufficient stirla<e "Jiiust "he W«v"i^e4 tclvueec\ UieetJ 
of <Jclt»aieA 'beajw Q_r\d %c- '^^cr on ^I'WtcV it re^$ To avoid mju- 
Y^ to either. A^dn ioc imaJx c. uir*: masi tt#t fcc U3«.<^ io su^o^vna 
queit Uaci. or ike t<eix5(«f> jper anii 4 a^£<2 «/* ixs c-v^^s Hficiton i?<- 
C437n.es safftctcrri to ru/jiun tf . 

/Sjress ts disirt hided /ercy . <tri</ ti^s tnien ?fiy ctian^ j^otrd cf 
i/ie area. i% 

camln^ M-J^^n iK<ri avea . If egi£al cJPs (ai( paxalUl} dci on e<jua/ 
fl^Fs of a jsLane sut/acf , -^it^ stress Is 5at<i-(oije ^f ittilfdrm infcn- 

vi'Aere P- f dt<j.( force and F th( "idtdi olY€xx over >ir/iio/i jf ii<f/s. l}t 
sie^m |7Y-e8sare ^k a /pi6t:<>n cs an e^-atn);!* of stress ^f unifcrtn in 

JSr ^TRESSES ONAHELtMt-HT, OVTWO KINDS ONLY 
Wktn a toUd hodn oj any ntaretrla/ is in e^*(.i/?ritt7w uno/ev a 
Sy«l5^cm of forces, wklck do uet ruj^tUre ii^ not (^riU is tfs sfiaj«>€ ol/- 
iered (ie.iis elements ore siraUg^/l, and sTresses jivociuceo^ flTi"iiis€ 
f>(an€5 on yukickikt (orcts aci , jsui dker stresses cU%o o-re induce cd 
on so?ne <?ra/^ iniertusX sar/^ac«« j4/^A;cii Separate cUtneni from d- 
€me«t,/cyer otn^si atoKeiKe forces v^tirk wliic/i fk^ c^emerrf^ mo.^ 
/lave cLcied on €ixek oik^r tefcre-tke af>jjlico:TioK of tkc exfcrna/ 
fffrejscs cv ^a)}jfUed forcf^s"). JSo lonq at ikt yj'kaU selid hiiii 
""{iSl fc^^y W-UdLer c^ n sic^€r ail 6'H , +h cs e * I n+cr rn.. * %'hrts «es , iei no ihn 
foTtes wii^i k^Atcii t kt hofiloYK en cnt «tV€ of (XJn*f ifnc^lntLT^ carina 
^Um^ otcts OH. "^/it jocrf ion onike dktr %ide , ^o nd apjjcar in aa^ e- 
Quaiion of e^tuiitriitm (for if tnfr»<ii«^>e<i! ^'key \i/«ui<l cancel ou^J; 
ttrf if M^€ cons4<ier fret a jpoi'l'ion onty, soTixe or aU of what oou,nd' 
iVJ^ surfaces ar€ cuttlno^ )»U7i*s ofikt original fccciy^f/cc 9^ess«s 
eKuiiH9 eu^to^e JbUt^^s are brenjW' iit/o i/iC e^4caiions df eom- 



§i8l £U£M. STRESSES, eic 



jSimiUrly if ^ s4h<j/« eUmeu^ of Hi€. hod^ is Treated h>j dsd-f/iltt 
siressei ou ait si)c 0^ ib faces ^~io<\^k€r vviiK ils wei^Ht, {jr?na i?<xittJi^ 
€ui jyair^m of f-crrces, ^le b^iy bcin^ su-bj^cise^/ d"f rest, 

As an e)taruj&u of tuHirn<il svYess, conslier cujatn ike cose o( a^od 
tuicuslott. Ft^. /^3 $|i«ws Hic wkol^ red (^r e^j e- bar) free, iKc for- 
ces P beiivg i4itf preisuyes of ik^ pWiUxikt e^es, ancl c<3UfcSln«es- 
"temai. stress /co7n)i>r€SsU«. kerej oniKe surfaces of on"fttc1". Ctncem 
ati<^\d secTuon 'mtJuic'iriroM.qk AB^ fdr etvottqk -{y^rvj itie eye ll-ic\l 
we ma^ coasUev me inTerna^ sKess lo pc cm<|*c?rm iu Tli«s Sc-c- 
tion, ctrvti consider fee "bo^fjon A6C as a. -fyee \)ocly , u% "ff^^. I'^t 

llie s^essei o\\ AB^ now cnc of 1^6 bcancVinu savfaces <?f l^^c 
•Jvee laodv;^ must ^t '^mllel t T;,!'^., normal \ AB ; roHner 

16 |>r€clucle<i \)^ Hie aecess'ify oj S^Y Ve»no ^ O^Aiid rt>es«|>* 
"^o^llToii ot uniformily.j Let F =- U^e SecUowal ctr^i:t/ A6 .atidL 
^« H\€ slresj. I^cr un«t of area. -, tiien 

iX" = gwes :E=r Fp , i.e. , -j. = X- Uj) 

Tine 5l^te c"( lnteyj^«.l sR-ees tben^ is Such f jiaf (?w j<?iaj2e5 Jber 
j^enoliWar "to (it? ojcts f?/ ifu^ fcar "^/t^ stress is feasKe and normgi 
(■fo fiiose ^Dlan^s). Si-nee tf a :&ecTtz>^ »»/^re ma^t M\(yij.e io tkt ax- 
is o( i\i€ hour, "/(le ^itess would ^illl foe jjcxraUe! ioike ox\s for 
reasons ds cthove ^ iv U e^lde^i: Huxl on ait QbUciie s«<rfioT\, -//it ^ress 

Tkc j^resfttce of {he ' iayK^ trixlal qy sfigfer lu^ sTress in oiltaue 
secdicn^ ts re,nder€4l eridcvd ^ onVtd^-Tiua -f fwit tf an obUqyue 
dore-4o4t jo'int wer^ curf ui ii\c rod, Fia. i0i5. ike %lte<xrlnQ sWs 
C^\ Irs surfaces Ttiaw fee ^ufftti^ni to o/erc6Vi\e fricf'un aiic( cause s/i- 
(Aui^ atong xke otu(?«f|?la7ie, 

Jf ft %kori )Qrlsn^a^'lt Uocl< U LLruicr mo cc^mbre.s&iv£ xdlow 
of "f-?» loic*«, eac/i-P anfl( alpjplUd ceniYat^ in ov\e tase^nrttTm^/ 
sAci^ tltoi ffie tfa-fe <)f iTd+eYTial airess is i/tc sanie <x,« ■/k<;t<' of i/t£ 
YOi/ unoUriension e^ct-j^i iiuit ffLi «#rnta( sire^sfit ore. ©jf cwdi^ir 



§;8/ BLEM. 3rRBS5B.S,dc. 



ri/ slqn^i.t- comhrts^'y-Ye iTisread of renziie^ and ikoi ike iliea.ri)va s^re*^- 
t^s (or iencfefvc'j -^osliae) OK ol3ti(^LLe l^ianis are ojopastire in direct (on to 
-fk<?se In "Hic rod. 

Since ike rtsMxid STre^s onaaiven ntceTrna! j^ici'Jie oj^ a tJoctvj 
{3 fMr(^ r€(>v&S£KTeo( c\j Its ncrrrvac auc( iangeiittal <u>mj)orie^is K/e 
are ikcrcforc jajfij^iecs/ iti coHstJertuA j^j^i wo nind'i of \nTerTiai 
riress. norvKixl or j\r?c t , <i=ci.^cl t^ticjefiti'dl or s>h£f|jrm^. 

182. RELATION BErWhRN 5TpHS6 AND STRAl^f. 

ro^ In Ten^iCi-^ . Coi^sidev -^r^t ^ smo.)! culojc element \rj)r\ose edqe. 
= OL irt Icnotk cind wKick }xa6 Twc ■[a.c£S jaavaliej Tc the )>'^j>^r_^ 
'htlrtcr token vitav tKe iT>\c)ic^le of ttie ro4 m j('^, I'^S. "Let ftcaw- 

€Ye<i To reivi^»vi u^^cKctrvi^cd MjVvjlfi tlie. Two -forces r ^^e act- 
\ny CIS W'for^ Jh^xY actioii . I ne ve sal Cant sXYe.53 oi Hie jaxe A6 
lie^'rv^ oj c»vv inrev^slty "b ~ TP-r F^ (^5ee eo^, iZj ^dcv umt erf lycms- 
\f<irse »ecJiO Y^ d\ rod ^ is ==r 1> Qa, 5t«^ ocJO/. Hence its component 
normcd to AB ts jba*5tnV anol "^te "i<xn^€niia( comjjonent = 

For ft, ro4 itv. sim(7)e te>rvs*ot^ we VvAve^ en «3«-)>la.o t nicvkivi^ ^^vtait- 

\<on jVuW*)© 1^ c^CvioriLS Itic nftTr»vt«.l ^r^-eSs W^ «4.M\t ef area of 

• na sTv-ciiJes ovc C"D are %t bame. u-v value cci or> AB 
voUOfi lor Be c^vul AB w-t ^w.l»4iltG^(e ^o''- c< for o( , Fl^, 

ly^jiljl^ e.;^a^^er<^][ej, ^ "tl'>6 $l-r<xcUs or c^rxtw^ae df ^oriA^- o^f fre 
y^ece Y^^<j*/"er5 di «r*^|V^«l '{orivi co»a^.JD ^cWy w^>«^^ tft oflcrnAl 



^_i8x_ CI^C/Vj. STRESSES h 

► )'ee o v^ /i » c/k / V tit oc>e f /i. e 5 h* e^-.^e 5 a re ?*e may e<{^ CoYr&sp dnd 

or may he so Cor>sicleye.d pr prCiC-tlcaU fiUfhos-e^ . St^fore. 
stra^in tni> ^dj^ AB Yi'as &(fii&i to <l ,^ a,s tk^ p\XQ% P (fif. 
i93J <^Te'^va^((ua.ll<^ incre^..^^.d ik-c ehn'^<xtUn or {iddCtional 
[e^n^irk of AB Ino'eases in Hie. sumeydUo^^ ds ti-e 'normal 
stress o-A 5C and /iB per unit of (irc!dL; jj scuiUar states- 
m^n\ vaxy fce wuzd^ oono^-nity^ fte e'(on^ca.uWu dfA TJ and ihe. 
^ress ccrre4j^\(i'i^^^ ia (^ ('. e, tl^e^mrrmi sfYt^ssonBC dnd 

jiy pgr mtof cre((or\ o.lipVTJi?A'eS- ffkis /> ^Ht in ami sfaft of 
She.%sj^ jhe-xj are, ^\'ldtntl\f at^iJitjifijiWe /0?' //?e sliearin^ strQin 
C^^ f3^' ^ke Qryafar di3MicT\,or iiyf^^rence^ 5^ between f^^'a^ii 

io.\N then, asT W'^'e^ses W(tlintf'k& li'mlf meitt(on&d ojoove^ 
(f VaWc-s jjroporttonaHjfob sin o(, cos (X^ 

/8Z, 0^. EI)f/l MPLt . Suppcsincj Hte red in CjUesU'Gn |/i^p^f> cf cc 
Knid a| vvoid in wlifcA q^ sh^^'i^y siress cj- Zoi IjjsMr. sc. (nek 
afonj tl^eorairij Or anornial shtsi of ^on liis.kerL^ inch per^ 
j^evdicuUr to a.'fil>re."J3{(]ir.e.wili pTodvxe Tiiptiirt^ recrahtd. 
ike yalue^ofoC tke an^l^y^luck-tkej^'cLln must rnaJfe^Wf-^k i'ne, 
avs mt-^ as V iy\tyta^£.^^ ijie ddncjev of rapture^f-rom each 
SOuraeTria.y Utke^S^-me^, This Wjiiire^stkcd lOdiH^t^V^bslwOi 
Cos^ : fy sin'^0( i.e. tan,<must z:: l.Ooo .\oi^ 
63x , If ike. cross s^<^ti07\ t^ftk^^ rod (s Z s^> inches ^ffie. 
^rce P ai- e(Lch ejid ri^^^^arij h Proluce. ncptui-e of elf her iQni 
wAert(i( = bSi: isf^uni h\j putttnj p sinoL cos<^=^ Zoo:. ' 
f^ 596 . fU. r>er scf^. inzk , VV/fenca ^sincc^p ^F-^T^ F~ JooJk 
[Unih incM and mind.) 

i^B.iiLASTlCITy ('y^e name. ffUtntoike. j>ro\)e,rU/ 
YVkccK Tiiost n]afertaUti(iye^t« a. cerfani extent^ of regaining 
ikeir orimdhrm i^ktHi&axf^ndl farces ^ceed (^certain l/mit 
c<illtdih^[:UWO Umr, tkiytco^^r^j of dTLgi'ncLl;f^-m 



5/S3. [lLIM. STRCSSiTS 



on^^e-parrof t/,ee/e^.e.f, :, o.\^ partial^ t'lt pcrmmentdefom^m. 
DeinjcoiH -me i L j ^ 

mAHc^Vt set b^corr^es v./.n niatl^ed ^'i fli^, sVft^^es ar^ «rcrea-- 
ed c^ri4 Iko rest p.c^e i^ ^wcv, an^-k "V.. f^y -coverv u^ l!.. 
InVcYvals of TiL'sl 

ll.e .SAFE L,,0,T 4 sE.«s:i;i.. ..,., ..,„, f],e eUsl^c 
Wit, cleTernnines V!^«i '^sil'i-'? S-tiilSjH <=■■' S«fc l=o4 «4 Ttie. b.«e 

^A^.u^U tTo,i \.e«,v,.s, f^vfJoDvi^ <yf n,e ^/ew'jersec, <? feel 
a~l IrCH Co 3«t T-er,lo„,_ ^^^ com|,..!«i ct^ «,e IK^eory tK«^ 
The, <^vear«t i,<,rm.d ^S-es, (t....MCK «r- «mi,,-e«,on) oc.<;^r«^v..c^ 
&ny mWroca ^tanfi sWaM -aot «jrceeci. lirtrti Us. Wf s<(, wJ,, 
T;«rT»>6 ^K-eaFcst s!ieav;«y sTi^esi -i^ot-o lUi j,e^- ^j. mdv 

lfr¥ Vj,. MO.D0UJS Of EUASTiCVTX C*o.v..Ws .afled" 
-Jxr «f,-,t cf ar««, 'cy fct ccrre5j>o.,4,«<^ vsWrtie strain 
tor.^ sul,j«r.ct fo « t.„s<o^ of ^i r-„„S = 5 0CO ^s ,t 

'.-on . n,.K £ .- (coca;) 4 6 . 1 : 300O «.^ J 

ft-Ntnei) h'Ai <^h mtensity of 

%= T*-;- F = 5000 -T ^ = iOcTTO Us. >e>- s^.U<l,^ 

t;-^ C^ IS ..rf n,e £««e <^u..,),Ty as > ^ [.e, lU, >.r s. 



"f- 



er 



§ )8^ £LEM. STKESSES 6_ 

o| ^VcLce. r Jn tVic stcLv^cT of str«hct)i o"J rnaTe vial^ Hie 
jncK 15 t-Ae mast canueriUat KnqlUh lintcur uni t, tuivtn tific 
)w3urui i5 fa^ «<u\ct of force ; 5#me(^/m€5 tA^ fovi an^^ton are 
used toye/Aer) 

*^^^ujrtti4flflt yr^n iftigttsidn^, inihe direcHcty of tha /lire, as 

S »<try ifi^etiker, fcr^pQ^n dneti-ictx m ao^ttfcn m«t<-naf, 

ttoH in a4toen4ftaftna.( £xj»«nmen.t' ctnfcrms ihtt a^ftrcxi- 

experiments on j/idr^ t/«ti^i. or on rttds cenfin^d lahrafi^ ia 

kkt sh^tina stress ptr WMtcfax^cL mthe ot»tito{iTtcWcii 
b^ $ ^in n- fnf asarc) t/»€ cot^^€/^n<3ima aAjM-lar strain 

or -/^v «K/e4rtPia la aM»iSJiimaf<^y Con^hsk^t fcr (I ^tvtn Jit- 

/^i* ISOTROPES TiH nam* «s ^tuf^nf© fn^rt<i(3 
fc^iticfi cu^e kamc^^nct^..^ a.s reqar4<'> i/ieiV tiasftc fifvoper 

irt«li(/t«Ct*i«f/y ^^esoimc fcr am^ i?(iKs;^'<jn. £.i3,, a red 
oi^ r^i6*r cuf* out Of o-iar^e nt^^^s (jy^K ^JkkHit tk^ 

ever rh or'vna/ (bc»4^0K /n Mt /n<4«rs. FtSnaus ma- 



pSS ELS.fA.£TRESSt:3 , f 

ways be coi^ioletfcd . F^i^ ' pf.'it*^ '-snd v*ei<l«-H^ Pi\i,\iyni^.\-CM% ^mdip^ 

'';ei4diiK^ ii^ aan.ou.Act xA^&t- ti-t- zi-x <:M:f^i^Jui%ci-?' 4 '^■'^'^'^■^~ ~^^-^^- <^^«-^ '^^'^^' Jvft ■ 
iuT-« &f Hit 'jTtalretlal^ 

/I7. SPM&RAl PR0PI:HTiES OF MATEHiAL$. lun^N. .f .<m. 
jt|i>iiilotis oi^feasi^ (ii4.dc' itfe ittAu £i3LA^ tiiat «it "master Wl ii^lif^iiis 

t- h pTciHe .U.U c^i^is aW cAsi iTi?^. , '^k^^uihr-^^; Wii%<iy« sft^vio- 

y^TSA. bui iinjsU^'S iiiti^ oriadk^ka t^KcevHitva'i'i%t street c?^ trlnniiv *t 

Hv* dii^k ivmit; itvis IfV'asWii cjifts E.^ far vfr^fe^M mn ISM^M 

d^vibl*- tke E^ l^tv ca.«i Irem., %'kdv +H« cGmjJs'^^^iN^^ S-he^-^es ^l^V^t- 

^ic^( )5urj>ff5t6 A/A^i^-rg fUorU^ /i?3i- aitrf oiWs of more n!c«ui(^ 
a^ 5^.^ic*aai( e*«c^^ wfc?u ii^^tr mWii>U art jjroi?e;rU dLrferm^WW 

*'/» i^t^i^efnin ("kt )>r<.«eivi:w«rk, a*t<3tajrt wmjiKXYaiiveUj «lmWc. }ix 
JCHfc* cuse.:. jTAjpiiic wil( i^ ^rfc^errti "ip avw-lvjltc mettc«i% a^ mete 



^jSS. _ ELEIVI. STRESSES ^^ 

odz \i^ Aiioove/red |or ckfahitii4| solaxton^, AaaiH.eitperiineni ts v-elisd 
0\\ al'moBi €?celu'jivel>j In CteAliua vwlm todies of ccrlaiu -f orju-i n-uc^er jjecu- 
xiat sv^srewN^ or hrte.^ ^ euttivtcoi f-or'nvu^Uf beiiwi pais<i oritke e?fJ9er"nMidk 
•m-aft^,' e,g. tie oolldjjslna ot h^^'dtr tube?>, avid in. sont dearte ijie flev^- 

/^(}. CLASS! FiCAT! ON OF CAUSES. MHiohqI tnccn^case wU- 
ever oj fie cle^onnftiton of a sollcf^N^ a l^akiricr-i sijsteni c I |oyc€-5 ad- 
Liva en VT noTruAi Qcr^^'^ile or conikit^^siifej and ^ilieaviuo sfve^ses are 
fcffik c(eYt![^pe<i ui everu eleuic'ni vi/liicu iti a^fe-cTed atou- (acajra ua to 
ilie l^iau^ section (^ow^idexecu cAses wfiere rlu bodl^ i^ ^Jrismaftc, tfif 
ocieriidt svjSteMi consisfina of Iwc eawi! aii^i oib^iife fofca oMt cd tack 
t^ of -fKe j^tece CLwdl dlWetfed awa<j |^runi€aok mker, are c^vatrunU colW 

cases of TEMSfON; l[ nie j?iete {3 asa^)n brU^i vvlllime sauteiwAier- 
vnuKxi fOTces ctiretied • fowgro l. eack o+W Tii<. ce.'ie U said -folse aKe of 

aulie Zona ( aohcj cotavjniy, is a ease ^^ FLBXURB. or bty^din^ o-s 
are a/ao w)si ta^es w/^ere-ifie ^A)3J;>ic€(i fottet,** annoi dixcet'ed (xlw 

ca5€S ^f SHEARIMS; a-fw/sW^OLfi cue ol TdRSION. lyAen-Hte 
Qrouyv.+\i |o»'«^^ d^t -to ike wetoairs of -fk eUmevus a^eolso c/>KJtcl- 
eY6o( a <ton<\r>l'noiicM oj-ksc oYmi>re o/t/i^ /oreaccun genemi Cixse^ 

in eacli case.a^Tr^a+ed.flte jjvinatai ooitw ahited ataxe^ soiode- 
stqu -fnc )oi6c< o^if-> iodAlm Hud ilte cire/aitesf atvc^s, In vvfiaWer Je- 
ineni if *^iavj occ^y, ^kcJl^iof e^tceed (X %a^ value ; ana ^onieftm^ Ai^ 
■fk«-tmor< f-fi Ltcveitt kbo qr£aT dte/ormo^Tlon ^u4fie JMtxiof fKc (otecf. 
rk*. fmf objecf f<jfo [^ovvie sw^Htcwetd STRENGTH ;Tk€ ^etoiMi 
^afficW ST/FFNBSS. 

/^^. TEMPERATURE STRESSES, if a^iet^ 1% uUnr suck 
cofi^Tmaluf ikaf if Is no"f fret io ckauci€ lit ^orvx wifri ckduafcj tf 
iekiberaiuye, e^+erH(3i I -farcer ate indu^eoi.-fkfc ^'ivesje/J trdducccf 
t^ w/iiftt aire cd((eo( tg^nj^cygfur^ &4ves5e$ . 



IIL 



xzmdm. 



n 



ENSiON. 

ip.HOQKE'S LA W BY EXPEJ^I/VIENT. /S^ a-K^icaUxj^mit^ 
pi^e teu5i«n c^alona rod ^ cL^tCU rtzetcd sucia^wrotLaW Irau^ctM 

biu^ MtcliawtcA Tilt t^i^cyimtnivi old isioAt h^^ ffcclQkins^^^ form 
ike Q^eai Itnailx. &f Hie yod^wklih mAt cf fttpiA^ki^ Irt^h and O.S tj tn. tn dU- 
ike v^trd// incY€aifi> In UttMi i>«l6wfite elasiic (tihif wtt*redujCi(i| m«»s- 

ib (hI^''<s' '/a/ttv. /4^f£r e<xc/i akjiyUeta.i'i^n uj loctJ ikeeiciiacdim 
was ^nm:9y.r€c(i oW dfirariy f^nmal cf Hu Lc^d.ike perni(^yheni ul, 



alle o{ elonaaii^n^ ej 



awrour|fc(-{roii tad, ofcileitQHi •'//(J'^'2^'^ 



X 



Ah 



TTTTTt 



IL 









2X 



3X 

// X 

sy. 
6 X 

S X 

^ X 

/ox 

// X 
>2 X 
eic. 



>7 



.33J 
.3p 

. SI 55 
.16Q 



' I. 






(tHci'US> 



.0665 

.0S6S 

.CS6 

.QSQ 

.06^5 

.082S 

.ssc 



0.000082 
.000186 

,ooodji^ 

.6COA7S 
.000 6/0 

.000/66 



0.0015 
.001 
.002] 
.00^ 
.OD/i 

.00/5 

.Clf(j 

./6^5 

.66? 



^iQf TENSION- /J_ 

IcoLd Iti on^ €^ pr^meni, F Hit tn^t ^edim cf-i^^ wd; feetictf tfer 

??i^ii^ ^f i^ ei^Xi^lm ^ sW/^ a4£> i^ eqmi if /ife<?4e's iiw ts 
Irvie. Jf Vi/iK ip-c n«iit«l? inihsrkJd<^ fLxL fhlt is ^t^ tuwriy huf 

if PanJ if^ are amj iwo Ucds fceU^ Hu t^, and X atui X, ik^ tmrc^- 

Hence cd fk< ?^ /6<i^,w1j(c/i t?ro<iac«s a^ens^iic threes onw 
cross sec^iOTi c^ j)-^8y{266/,S^^/3l/0*0 (is. I^r 5a.ijic/t, ft? 

fcirm^nt are j^^curcJiei it rU axis of iive yoo( , iv^e Akc^ tiial tf U 




(^ ff/i^ iU MsddM^M^mihi ^ tea*. ^n't^^ 

Tk« vaUcs of £^ coanjs'aieo/ /rem €x)?6rin»CKK /ike -HtoW 






/"^Exj£>€r, Eg^'H^^A^ OOO lbs. ^^. in. 
5^ M E^ ^ ^2l£U>q CC^ - 
^^ n t^^ n ^Zl Bm OM n ^> 
If shnlitcr Q^iKLJiiid^flmi^ wzre ynrodc h^tsM^ "Hi<^ eUrkd 

siWrivKer, skoYVtiuj ik& Tn^fcTWfr l?t' ^UidmA uni-ci ituDVc Ti&xoitij. 
^.iUt eicucj flu u fills i<t^ o^ aJ7$cuia^,^e <ft^>va {i^'fu.( ora^kicre- 

fia trior of si^ki 'xu<i 05.%-^ liari. , 4f '/ft^ rc^j^ecrive -elastic 
f iitiifs 658, cW B'^^ l'-^ w({( be no4ite^ iii(dV^^ tuSMt fcr 

cjlrwe, olib^s cu^TKe aw<xM <»^v^Ye qraiiuAttM ; "{W "i4c curve ^r 
S"/Te.e( iU^ ntaxer fke a>cU 'flut'u'f^ cik^ri wliicli indie otits 
a /iccjlzer va/u.€ fcr £^ « aHc:^ -fW -(/te ordinahs BA';, B'y4'^ 

Si) iVicix) i\iAlc<r(-€ -H^t -tetisiU sf-u-^s aftlu; "tld^iic /iniiil. T/iesi 
(afi^ oiMJoMiie'i wtK fee coi/e^ ^k^ 'moduli rf ^<^t^aci4\i dj'glgs- 
1*^ ii^^Cf for TKe rfi.^j>e<ff\v€ mo:^eria(«. 

Vy/R4vi - /A^ e/<x<?kc (^mj'-f -//k curMt^ are iiearlj s+raiflW 
(jpToyi><^ H •o k<*> (aw) aiic^ if f^^^y ^^c( oC'' are 1^^ an<^ic3 »>cdf 



mS ■ ^ T^miMi -r-:— 2^ 

fE. I^^Y Vii.kt>v»):^£. r.Jtr?n^JL|£^ jfW-/atott« J"f/t^^ 
as A qrct/j-liu'i! re(<3t1lt?ri h'i-^^^rt.'n. tketTr:xiiA.iJi t-f e(*5fii<jt,|v: 

vujbfojr^ cxtcxtrs a:(as-fre^ c j ^"3 iC-C lin. per ^'p mck ^f mm- 

Tu'MuY*^; e.<'.c tti:' xtarh^ir-) and afirtaytldhi^ ^Ufxj^odUrn '' 
^2=:^ ai:?£;u:i C,30 cr 30% . (TAf brtc^diiw iahU nk/^^% 
cv [if a peri I on of Hie re, s it i h) Tk c (ticni ^ si^ti^ 5 /u^t^i 

(.]U< 0.H <j0i\MH(jii (xi: tixblijjii cf O-htui // cr 5 % , wAt^* 

inc^ an ex4rfm<f €t<?ti.a(:rfun cf fnrm W ip ^6 % , Th^it 

fereoikivwj sfn^sscs mnc|e ^ygyu. JO 000 fo l56i)C0 lis, cr 

tk^r^^tci at ruj^iikt^ a:n. dM-nMTi{;% of cnU 3 ^r/y iforfib 
ii|(Litl ,^ceij,(, ific' yuhiccriua sire-^i, b^t-iuj abnif tSOddih. 
pe^ :k^.iucL> Tiic cl^sjk iimd U t^itk^r tU d«fh%tdf in 

ixyid ik^ mc'de of rtux^iiu-fcuthae ha\tc niM^t^k t-Hfluince^h 

of prhr\%.% cf nemlsj aXi kUii^ frf m-ciierldj , acc<^m^f»' 
v•a^ ike e^cnaoiiicw ofUuHik is fcunxa. a'so a c(tmiu«.fto»r 
i^f y^Cdik wii4»5€ rciatL$^ amount IktIu ta'^e ofikt ii^ree 
V'^€^'<kk Jw^zi-^r^aUA i%abd)xi. i~f>^-/: of Hit reUilw €- 
Uu4taiiion (wiHiiu elasiic (tinii^. Tkut in'tm'thiTd ^x- 







i 4 



Ix 



ax 



$ m 



•!_„ 




I < 




i^ § 207 i ,I_| 



fi^r^.d'?' 






E 



1 - . 



=^rH 










208 



§ ^'^ 



§/^3 TENSION. IS, 

b€Tiw\<ni in iKeioifc iA §l(jl, fhii Yelarti\i€ lo^eraXc^n- 
iTac+i©n or decrease oj dicaneieT -^'i^o4: afC ^Le^aiwd 
0^QCC02^ In Hie cas£ ofc&i^flron o^wJlwcrcl ^k^eeUik^ 

ike itLor^ duciile J^^iat as^wpuJtf iron a^iki sp^fsWj> 

SO ^6^% ai ikt fx4ijcJiLre . 

rf ar Dcl Cf duediU mciai as u<^ f fce j?re c€<3ftHq ^aWt d^, wt 
/(j^. MODULI OF TEHACnX , Tkci,n$iU shes, f^ 

-fure a^rtsw^i 6»J^a oiKM }xuxi^'i^ wii( be de^^dtd few T ^W 

hrnii fnoM ^1 c^iitd T^' T/^c rccJic erf T io T^ Is n^fi 
{i-(^d ill practice hiJ di.p^nti'^ u^^u cLttiA^^siance^. 

J>ui^ tr ii}4xd r^y a-Aa k<SL^ asedu^ncLi area ^ F, w^ /iav< 
P^FTJor fke uHrnude or hreaki^Lq itrad 1 



%IU TENSION ^ 

1*?6, RESaitNCE or A 5TB£TCHED Pf? ISM . fi^, ^o:^ 
In tKii qrcxiiuiil 5lv£}ck*«v c?^ a btVsm^ -fitted ^t on^ exlreiWAy, 
ike v^lite cf Use to^j^^U Wee^ at tHe ol^r necessarily dej>e«<is 
on ^e eloni^afHui X ci eock i'ti--^.^ ^.| |W si^or&ntm^ accord » 
,.W to the Wioiia ^ ^ pi_ ^^^^ ^,^ j^^. ^^_ ,3^ 

vv^IVau tW slsjlji; UmiC, r IT v-^e J?We a. Wet^Vit (^ <m tie 

4 IcoKjeS o] iii^ vm§ireickif«i jerUva itx^ then U^ve it'io-(neA^^a.u o{ oroar* 

Bui fran^ ij[>) P"^ FT" , W (see §| l8/f oW Kjl) 

X-d 

v.;|i^rc V i-i tKc <ioluTne of "!:[(<: brlstti . TKf ^iiait+L^ ^T*'C'\o^ 
y^cxk dtyin vtLZ'\rid^tkli^&x<iMi9 da^Tiz jnni'l a tabic Ivxh o-f+lif 

i{n\e vTv vrfc'i.ii?.i'V;Q to Wml c^o.>TiC 4i'^^'^U b^^/s^s o4 ike sa'me iylq- 

of -cue 0-f tke inanaU^ su.cHd-s O^^B , O-h'' Q" Kxxjia.ZOO ; ^qx 
cUHic (fm»"i^^ bn OA^ . Tkt Tiitptaiueit^j o( jr^e (xtea OBC i***- 
tW: ^iasftc Limn Itjfke )^>cnit o\ TubKt^f -for ^<xck vi?t+i(ULL sjri^ 



3l<li TEMSION. a. 

I.e. 4!t€ vvoifk dene b>j ^kx s"Keis h oivottt {ctee cf a cvtbic tucii 
rKYCUcjk ilife <!lU4a-&ce it ^ err intT^rfveiiV of elxnx^tff^on . 

4 ic cTv eTa>| of Q ^ v.'U tk — at boik bt.aVWiTia (fiwieni a f IKt is- 

Snue P| — ^G , t,e. W ^ fi ,4'Kc wcAAkr dices tui reisrtditv itvilu'i 

-fad: , 4fie ytvd+Ioi\ W koirTrKmic (se^* §§ 5"0 aa<i I Soy TkeofCtu- 
ai^^j 4kt elastic ImH 110+ beVna |;dt4ed[ , fit^ cs<it/(Aii:>-H% 

Hence a lc<3ui & *siMidi^\j aW^(ie(i otcaVions dlouiU Hw 
tt'YLSicu x+wouU l^<uiu|>el(£d[ +Di>bk(Jt(bjt^taii\j bvj a ^atJ>or|- wi- 
der Tveoclk , ¥vluJlk U VtffI Ye«*)i6H*(i UTxKi ijtc +eu.5iOU 15 lUft ^ &. 

I^ ttt vy^laM & sCvik^ 4krc\tA akci<)ki -k before sirlkUwi 

G.CK+K,)=iP.X, (.6) 

i^7.SrRETCHiK6 OF A PRISM B\ ITS OWN Wam 
In rkt cofc«« #f av<inj IcKci Wrm ^ucii a^^nl'^^^a~bu•nl^\t<3(,ife 
wei<ih*V •mu*'} b* 4iaK«n\ iv.\o a^t^xmi <t^wel(as +bal office +er 
Vn\ua( (caA P, ; s€< fioj.103. At (ou) ilw j?nrm bsUwi,iwt(s 
uutUix\>»e<i fccwdiiicn , (rf (b^ ^KaWecl bM+kc looujt TJ aitclii^ 



I: 



§J^7 .._ , TE-NSiON- li 

a">vc^ % -fTom is 

(See e<j. ^l) S 1C||); «bte< P» «v Fyx is-J-U Uac( KaiviSiu*^ iiL|;?<;i»ik« 
cvo$^ $<MiXio^\ai:'<rka"l U<iaUi^. E(^u.<xt <iK%-fUr«|-i»^€ are was- 

J,t.^ A r-tke aivounH c^ue4o R-^ bUa an e>-'ievtsun ^a<IucA liA-(f l^^ 
Own v»/fi<fiW wc'kW j{>r«c(a«e liajui <diie U^cr ^wbfet^vl^^ 

i'l% a fori, 60 Inc) t i lai' es 4- <^l Kc c( ^ ^or iraax ( cw of f^ t p t ^e , a^'ii5( 

h?.f. yeja-iive eiouqo.ti&^ v~a)\ r ({k ^Se^ e^.O)J; '^^^'^'^^'•^ V(xyiQiU, 
,].a3r iiowUre 0xdieedl a sa|^^, mU^*- 6'*T'-v Ef {^§ /^/ ariJ l(j//). 
New tH '-^tfiarievt '«/<s»Ue i)| "Hve fo-ii^ ^A tcJjc^ b\j (n$J5eti.t"iii^ 
t^-Ojy i"S see-Kvio fc^ <M iU a^ijj<:r te^id wWe % ^l. T^^ /^'■»'- 
|>eY cv(?«^ 8 e civ on Fj I'^v'o.GWealcaal P^ ^ is ika.s 'j^i>uHci. 

IfS. SOLID OF UNIFORM STRENTH iW TENSION. 
or hm3^ feiii, ^.f M^^l^lyv^^f^ reciter iai ^ut^JpoYtiii^'vis d>^h 
.VL^HJliL"^ ^I!:4. ivHnnt^l (o^^a^ j^ . Let If ii^ et^ftUd (9-^ rev 6 (u- 

(ovv^r ex.TV-€mVW jb^o^f^ ti^ sct-fd ld<tii F T^ evervj Klint^tci el- 
a-fR==FT' . iO 



in wfeicA. {X dthoii^ M\£ w<^<3^f ofrte ji^orH^ac of ffu -scitd. Ixlowp. 

CO one((/y),' i.e. . ^ y;it v 

ciuc( i>€<xYtuj:j4)u same xaiiot'o V* (cd elcu^Kc Uniit"), a-s T'oior^ 

U^ij.TEHSlLE STRESSES INDUCED BH TEMPFf?- 

AT0RE. r-f -fi^e -^wvo etxdts: oj abri^'m. ave iwtnovaWl^ fijc€^,wien 

hcpoTkoivoul Iv'flv.c |o^it vi^Htm^i^eva-Uar^^ (yvdHin eia^iic tmiQ, If 
fcY <x ri'i^? OY foiK oj l^ Fakv. (or CW.}oc iAntf cf l^na"//* of ikf 

ameuut X ^-'^i^rtO 'iurtvujike givfu jtxK of fem|?erai«A»e if 
cit< <v<( wu^ free. Hen<i.e i/ "fii » (^on^ra^iion is js>rfv^tt^*^<^ 
bu |ii<hi<*^ \>oii\ VILA'S , -f fv-e r<5di ^ufi fc< u-ac^t aTt-v-tlor*. P, t^uftl 
in va/ut ■to+rv* fpvc.^ wkick wcnia h^ y^ce^so-iu f» f;>o<liu^e {\ie ?.i<m- 



im TENSiON. 20 

ojmpress/on'of short blocks . 

JiOO. SHORT AND LONC COLUMNS. Inaj^riim inienjiow, 
-tie^ trf al>|>lkc«t44«n ^f "Hie joair of €ic+cntft.t (orC4?$ (rr^xlufiUc {kt tbii- 

"Hie eicreynfli/ fo^cetjj anaH< j^nsm v?iia>/ tc ^^atv>j ctvvatt wi^«*«t 
vCfioiina "Hu^ sJoftrii^Kf. Buf i^ fit twe oiterual (t^fct^ axe dUiefit- 

l»j ^)u>W, (i^f tmU^s n<^nfe4r*<A« jbolH'^ ^f /«t«Tat tk^jj^nrt are broyidlftv 
Weuct -fte </ff"(-(«ieTiou fcrfween sWrf blocks diwi (otu ^fu'm) !!. 

»eciw>H -f/i< WtfdfS iroj^c^ /jchty oi^tii -Hiree orfflu.Tiimcs a^fcn^ ot* 

i(3/. NOTAT/ON FOR COMPl?£SSiO/V- Sx| u«ixj andhar 
sutacribt, we Ivw/e f or ctnL^jression 

Moo(w.(u8 o-f Elcj,iidf\^ ~ £^ ; 
wkilt we Y»iAv WY{(-c 

C ^ir ikt Modular of CrtAj^kiYiQ , 

C- for )i » cf sajt conijireszvKn , Mxd 

For fiu dbjpluft anrf Yeto.'fut dkoyf^mnq i^n leuqlt we maijalal. 






,4/30 |W at)Nv1 bioci\ 






?.^U't |#:'fc id eiasiie. Itmi' 



S<^fe eo-;rb:}s^.au^i foYcf' '-^ FC . J 



a.) 



50..?. REMARKS ON CRUSHiUa^ /t.t m §|?,? fcrdm^ik 

arrets, t^o jtr aoomptc^jVve ^tresi Vyi?i\Vi,v^' |,'ri?Yie' Vi^ d^kecfetlfYj^ *!mi 
i!i^: iilx^t bior^k, 1^ behiQ tfie a*yi\|i>e"i?jwrn J3<^t sa-^ii A}'a?ai«f fraA^'- 
'ikch^ hUces axe jorud oui |y«?"in.H(u ^W*^'^. Hcn^ € fk i;i,e<:.ev;t4J^ 
:.f ma.ki!^a i-kf blcsck ih-vef c-r |vx/.,y tuiucij as-, l^'i^a tV'^Ht/tde, ^Ijice oik- 
<^ 1 •filial ikt |fu;ftDVL t)U tk^ ctid'^ vvouU <!i(Uu'4e "itc 3lec4+oi.Uwa 

bxlcjixuj ^ Uferali^ , reuembil-uq bU^^xe ^6(iw touttihai (U "Hits res- 



unisU'v^ , m ik^- ^''-^H o| 'V^T*'U.<jk"t iro^ (Uvi sWl . Pot eacii ^f H« 
3a'»ue \y\H(xii> (XmA j^r c^^X i\ov. W 'rs aUc -t&u,'«,e( ^lidt |i^~- Ej 

EXAMPLES IHTlHS\OH ilC0t^PRB5SldH. 
203. TA3L£S FOR TENSION AHD CQNIPP.B^SIOU. 

TK< T»«.Kvcl Tvunifeers of ike j~oilci>tti.n<iiixtU art Tob&iak«n4S 



^S03 EXAMPLES mlEnSlOH^C'OMPR£.5&. U 




to 
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C> N> o c> 

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(The Qtojf^c awd deaUh t>f tt« )?ve^e^l■i w^rk aJ-N^ili: ofixolHi- 
u\Q lucre . F-ar ahu^i^da.vc\ dttdJii o^ike ve^uWi o^f^e ^^itote iw- 

■fhc receiCt works »| Piroi(s.TKu.rstDn, Buvf,L4iVicXja.n<i^aflQ 
An<^i'u*r coUunti mvofi^ liav« l^en (tMed Qivlna Hu Modulus 
o^ fie5tllieiic€ i-n eacK <<?«€ , yt-^. ; ^ £*'T*(wiiltk also = -X^Jj 



F ri^;; — — ■ -: — "- — ^ — ? — '-^^ 

tj , I , And I ^ .jVf. Kjincn In \itmi\A-i ^>6v- S'^uwi-t 



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MO^ EX A MPLES^^lKXEJmJk COMPRESS, Z± 

E^votngt 2. Tu%iiU inf t,\(s.\i(yt o| '4W^ Sieei^' f-Drtk 
•llvj -3. .21 fi. U>M^ a\vd 5..0a iu.X LlO'iu. tnut."ii(m< A+ifu ek-r 

ib. p«.t ^^^U\.cfv. ^^<?<5tl\fikt ^Am^. result -['(,¥ E^ WPiili toujpdUv 
^iKxxi "Hvc wtuU work «;<^ev.(ieiU 5j'Ktickwc| "tfetkeeiailiclhtii i1^^ 



-q {j^WiA, '^^.0000120 J (C^xd, %.caU') From §IM> v<e Uv€, &f|ore^s- 



•i!i^-- i^lv-Ji » 



t1-5 middlt Yc«i upoA ^Vpne tne.'f^ii, T-^.quived iae Wiiott^d^^^ \i^(L\i\^ 

il s fi HiU< 6" . M. ovY 1 6 WQ ruust 0. vvj T ooAki IT on roi U , 5 aV putt* 
f;i vfvl.tr, <xU>j ai iH ujij-jec «vicl/fD .Weak w'lik Ik om\ w«\c^Wi ? 



3J^0k £MM-EiES \HTMki^A^JlB3A^^. ^l. 

Ei-ygtiTipty 6. Ot)£ voiiss^;/ ^1 au ar^k-ttv^ Ptc^^^cs in ^teUillj>^^' 
W^tll a f oree of ^Q toK-^^tit \q\vA MhW^, aiu./W'^ of ^^^f-fed; ■ 

ioar. FACTOR OF 3AfET\: Wk^u.a^ luH^^ tA'^.t pf $W, 
tK? viiwe o| tic ^r^^i a'i ii« 4aw^U Ui^ti-U ^fym u,^^JteY^^^ 

r^v dou£ ^-f? 5/uti((!^ nol bt it^^ihau 10 ^ i.^v C -~ C '^"tj 5 (fee E-/.^ 

206.^ PRACTICALNOTES- If s^c^i <L%ao^^^d in^ej^^^- 

1 Afi^u-^kt Invi udk we've $iralfted ^VtsuktoJbl^ b-c-joVv^ ftc cUsllc im- 

Wiuu artiales 9| c^t^t itou ot^ W^W^i^iUv cxuie of acYx andsui- 

' < (, p ett j ,D f weidJ u<]* B el »^ iHoal<&«t bit^ ii I ^ u^tUi, •M^ki^i.U. Mil 

By l^iicyu.^ il'nvdi'J^ vv^ lA^n tiers W-ci "Hi^ jA^ci^ ^'e-ce^vlW^tltstov'- 
YTva« U. c^vtsicic'fabK^ W«low I (^C*y C .1 t/vc Hvar.oev ol tkf^•e-■Hti^li.*i1»«c^- 
•-'v•5arv cl biv;Ju^:.e Tii^'^ture b^lnfl <icb(iiA,i^,>it bci'fi&uH^e nxiA'^c <?fv«iy^" 
ro\ e?<-<xrApu, lU'll^e c^-Jv: o{- PkcievM^ i-?ou \vite\v^U>\. tup ,■''>-» t 
i^ i > pVi*^du-6^.«i h\i ■i^u.'viiu^ flit '■j.he.'b'* 't'D vct«u frDU'v *to ^;2,2oO ti?. 



§S q6 EXAMPLES - W TEM 3, kCChAPR^c S^^ i ( 

fj^TirCiiii were *K<ui« <vi*d( ike ^^tMjf^'^ lUracL^it^^ db-t5Utv^^ji3'4«^« ^ 

twee>L-(i« Unaii^ qhrn^ WW ^^^t i^|y^? tfe 'daedal (ft^»f 
Butts M^i^cridU ^^ faM^c^fitf) 

( ^"^^ n^^^ ttn^^M moo Tcmlai 

[frtaa 3^ 2£^ Con? j^- fe 3^-8^0 "H-'f^i^jr. 
I ^> 3X5^ Tens. iaS$CCO v 

2(^J, RIVETS T/ie aw^jo-Ut cU^iotiirji^li: .<i^ ^^a^ 

iH iU cijeTpvettU t>f a h&d^ U ^}?<4i«tt^ "b l?e prN*ii:i ^^r \\\ tb case 







% ^07 SHEA8)fslQ X-^ 

The let^vin^ or sKearinG <Jul <rf llie- "bart of tKe j^lale Ijefweff^ 

J or economy «f moterial tKe seaw ovjom£ «'hoa\(5 Ije rjoi^-^ove 

«^{ Uiisik "force eo the jdint l>t » Q-> £«icK ri'vct Ace also ¥^\ 
2OS3 ^^exl,o5.A r„ eock of two of If* secf.i^S to a sUav a/ 
•^ ^,, hence for safeVy AjaiV,st tKearm^ of vWcts we wC 

^Qi^ f ^oiV- ..oj 

Alp or.£ row of rw.ls i« H,e m««, Vlat« Hv* Mct.^'n^I d,»<a 4yve- 

Q=c^-2<i)tr' (r; 

^4 tut%-c'".^e.i uiu^^tis •* 



•^Wnee fe <l^e ca.4.„,io,v^ N »;ac 4 ri.e rivet 1,,^ ,'.«. 



^ f^;.e edge of N.e >i„f ., vtLr^ -.eK4lea U lifu^^^i 

b.^.(]«tl, ferine cover- f>)are wei,KS-t },<,ve ^Q ^ 
• <mJL Ctci < ^ Q ^ < 



If >ft Twetj don<* -:. iKcr Ules closely a Uy«p 

5o^. SHEARING TD)ST(5RT)0-^. TUcU„3e,f4,^ 

wj» b«^ea%uT.d in IT- Treasure. TK;4 •r^^ular cU.,)e«-<i;flb- 



^%g(?g . ^HEAfimg. p 

its value i?€(«rt "siram, wl!Li«<uxJiIi^.a4^ 

TJi^ v<».(v».^ ^f E5 I*'' dU-^erai^^$til>4«^<s£5 r«'ml>si<!A^i^[d«- 
iloifv o-H f kc bowuilna jj lanes ^f ^ eknteuT ci>usldl6Ye<i5€Uft.^ 
In |i(^, i08, <| aualiiftT ^em^T wane ^^^<kt^<^ wifiiutit^ Wi« 
IUt^j ^ho lAn atvi vtfiWvHs jsW^t dk ii^ wiit "Wift^c o^^n. ftnt, 

y«ket% 4f.»fc*VU. «r e<rmi5«*mx< sireeses «i€ also ^r^ieivr 015 flu 
some -Cct^es . 

j?Of S«£;ilt|f(e. STRESS IS ALWAYS OF THE SAME 
INTENSITY OK THE FOUiE FACES OF Aft ELEMENT 
(By ndtjKsii^'i's^nveascf per umi o^ gr^ ; {^<{ iftiJ foiLT ^Ws 
Te-{^'y reii +» axe ^^e l^e^ j^^rndtcickDr 4i>4i« Jsajjex bi +ia,-26^,^€ 
ske<xrv>ui -stress t^h^i^ jkuoiiti fo -fii€ j;jOLJ?<jr.) 

Ltt" etc aiid 3z. be i:V^ wlfltk a»(^ keldfei c^^llte elemenf 

W>«T , L-t~i +ti. infcx^il^j ot\^^ %\^\' t« tie Tia{it dawd fiti 
W =i^^ t(^oa bw flte "t&p |(3ure :=r t TKtn |oYifve ele^etif <xs 
gt I ret ijo(i>j, "fo-kincj mewjeft^s ato^ct 4Jied)cW b€YJDe'K(ivc*»'Ur 
U jpajjcr ,vy€ kave 



JiL2i 



^REAKIM. 



M 



£v2n 1 1- mere w^e aUo 4^$^lmi5 ^ a>^i frrcsst djis) oh cut or-U-Si 
^bdrj r.| ioja&ir4Wf ;i%crte^cj4^ xiio^ci d:wfc*kW Wcsnce (^«Y-f<H!i« 



iVlateriai 


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>.1>«-Si^^i«- 


tijs.sjj.ia. 




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qooo QOD 




JC €06 


HaW ^«£i 


^.0d32 


/j5.om 


qo&^O 


Casi Iron 


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1 0^ Ci^O 


15000 


20 000 


Wrs'i Iran 


^.C^22 


q om om 


10 ooc 


so coo 


Brass 




^ii'ocua 






^lass 




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iSOCi 








u iooc 


■j«fi^5ii,aic»gf 








500 


fikelj 






U 1200 

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OS mucii oa 5£5 >wcei4r Ivt jjHXfKcaiirr ea.5.€^ 4uiei>\dLtwiii< -Hue 



i^\ 



P^Siirtl 



§212 :SHEAmHa^ .,. .^.3^ 

fit rod. is tii."^*imon -v¥i4y^f4l><^ <i;^^ 

b^j Pri^t. BAtrr* Takni^ <ut f |€;fe^i4«i ^e^*^ ^'J^ f^ ^4' *'H 
under snhresi^ ^ItZle "ticrhoa^^^r-ei'ike feitf dit«i&?usi CiDnirsxi^ 

for , -kkiiva CA =:-u»iK ^ AE^ io^ Ai>-AI^^4E' Er , N^ir^ 
jE^^)^ Ju^U^^o^wlWi^i^'ceritt^ sir^sse^ ^eit^iufi tte eft 

jttUHfil tJiiii ^u+e^^Slt1Ttl^t ratio m;e was r:^^^^^ 



§:^f2 S HEARIMQ 5! 

( ^) ^ jKen F , ^U ouU \>e I 5 OCX) COO Tc IT^iX^ C>0 O wUdr 

2i3. EXAMPLES mpHFABW^. 

^^rd <i^au%st tke sK^-Cfno^ (jf-f ^ olono fti e gTna>n: ^ <rf tke* tor- 

tie 11 ctb , oj a v\/oo4.en He-^^ ^%t -^orce x T>€it%g^ == A ioaS. 

ar\3 t^e "wixi tk <?| the t*e — 4- '^^f^^ipt - ""CTsiW <x vaWe oj" 

p ^ jQO Tlss, "^e-r so. jnckj ««£ ^ WS' ^ J^OOC co^ Ii^\ 

i ^xaitib U -21 . A -i- in- fiir^ of w^unaKt iroti/tn m^\<^U 
l Jtea.T ^sec Kq.2CSj Jtas au ^itiviuait sk«<!b'm<j ^hr&njdk 

For sa^f^,J?u.Httt^ B'^M^a tmieoA of S^p^Eoo'iix 



'At CfiK 



M-^U^ ore ^ m*4Udk cuva -ik^ it^K^it ^tu on iU loini 
~ incii r Iv'efs i?e s^fltceci civ cn^ row , birrf itw S r: ^000 



1Z50 l^%.^.6CC% :zLSASi^^Ue^^ x^SJJ^i^nJm^, nk4i 

i^i Wt ? . 

In . rti^as^yz^^^ iiki^^) Str^MSS ;^i<fti of J^iai^s - 

side ^f joidj^ i| Q. r:: 3i) £^00 Ufs. ? Thi namW <?f 
rivefs -=: ? Here e^ck rvv^^t ^^iivxi^mbie, s^fi^oT aud Im^ 

tWie^re adiou^bU air^ntft^ a^xejo^ds S-lica^, Bi oLoabU 
-ib^T ike, ia.|-e sl^-eiftatk df-e^^ rivet ^ 2FS ^52^ y?s. 
Now 3£)D^0 43540 d^^.2 , sa^ q.C . Witk +(i£ nine meb 
In o^c row tii« rt<k\jLcm s^tiioK of tfce insic(e jsUfe ^ 

H^nce rUn^ mets uv one row are suj^j^toiejir^. 

C4ai?. H. Tors ion- 
2IJ^. AUaiE OF T0R510N AND OF HELIX. Wbn 

a cA|tiudrLc<3Lt tea%H or^|i43i|l b e4iLb jecied -U^iiwi^^hlic) 
Or "ix^vtn'iTTitai aciiou, i-e* wttealf l^i^ie me-ctiR^ of fcoUinij 

tcnvaiu^ eiraiokt audi -Hte eiesiiarfs oloua li ^ly^t-rtencc-vui 
%Kes"$ (v^kev^t^ Umcuj be c<xlled ike ^^Uiu t^f itoiv^i^-p^J wlwk 
ite i^ou..^ i^naijiall^ b^au^l tt> If os^uiut 4rka -Perm ijf Wi- 

















5 MP 




R^.«i^ ^^'<$ 






..*"*A 







fiZm TORSION 55 

all^j riQlii auaU^J tiie amoani c] ci.U4orf(on. fc*Int[ o-Sii inn feci 

vcxiial ,i^o in (»joVi3etu"tiv£4irciitsve»«e secitons, a)»c( "flic o^iieir 
two I^Kae-hf 4^ iwo-eonsecuiive <uraxicKr (i\j/{)i^ers V¥f?i?s<; 
com7no>\ ooci^ U ilial: o| ffte §liaff. £.0. in Fi<^.^l:2 we ho^yi 
ail {Axsfraoteci ekaf^, wlui^ t^i Ficj.il ^ If fields ili€ iwo Cou- 
pler (o|- e^ualTtvomen'tPa = ^bj ix eqiuubrVuTit. Tlie-se cck- 
^Us 0.0+ \u jaarauel blaues bet jpoidiculctr ToTkt clxIs d| tlit- 

i-n j-ta^ftwa^ ciii'ire^ Tialtf-analeii is noyv dUiorhd. Ivuo o-f lb an- 
oks Kave Utn hureat€c( , ivuo dlmhuslied fctj ov aniPitiLt 5, <li€ 
(XUflU b«iv^6€n M^e Utu and aline ^ralU 1 to ■tite.a)cU. SttjoJ5o>- 

-Hilt duiauce b^mcj e, axy otite^ e(emijd at a (it^faiice 2- frwii 

Tf now we draw OS' j^ardi/lel to OA^ tAe au<j/^ BOB^-n^ 
/s cAaeo( ike ^UG^LE OFTORSlQHjV'Aiiie S vxmkealU 
Tixe /ie(v.^ au^( gj iite p>r7uer Uef m ot trans vey-9£. pone ,t^ 
latier In a j^/ante -ia'>'^q<^n"t io+k'€. cglbdlc'r , ^ow "^r 
tau (5 :=^(arc 6B') -f c ; i3ut arc BB^-t<^i .^encc^putiiHC^ 
<J |W4aH<5, ^^ 

2/5". SHEARINfi SrRESS ^N TH£ ELEMENTS. 

tv.d( -sW^^^e^ ex€rfe<:)( ou t^i- b>j ck ue'tojtWs tn tk« four ^es 

«lie[( in wKicl\ ike ^leiitei^t ia sitwaied . Con.'&Ueir ilie^c 
HeiahboriKQ eie-jn^Hf^ 0'( ati outiUf d^yievC^ removed, Aut;/ 
"ite ^^ret^es but tw ; iA.e (afiey ore accoimfdWe ^dt ~tk«, <ii.s- 
toriio'n ot ike e(^vneut AuoL so fioU li Iv. e^ uiUbviuw . Ft<3. 
Zili skoyvs i/iU eleTuent'^^free". WtlVln +U eU^^iic (imii 



%2I5 SHEARlNd 34 




Wt«, "tA -ilMit yiK*aiules , Twt'*" h, ike slua!rirx:j -stress £)>t^ ^ace »f 
twi tltmt»ti wbicll fofiti^ fitteirf of^xitaKt^vtTi?^ s^Un and vifkosedyk- 

-(k* 'Wat diuor m\ ike -face b ti F^ dif UVm iie area «^^ |otf€. 

2/6. TORSIONAL STREt(&TH. vv^at^ Tio^tcA^in^^- 
Ha. il3 a>^[Mi[4x.rt UWti^k'+wt cMcbfes anic^Y^VitervvvriUlefl- 

ttijtc^ Tttimi^tr ^ <iP^* :5 ^-^ itivs^ art e>^o^eeL hu ot (in eltinveict; sd 

4-piF = Pa;9r,Mfe.=.Pft (3) 

esi: sIuayIm sK<«s (Kiitotedl b^ tU WVi«maI coi^c , wiu5e moment^ 

P^ U tAlUi ^k* M0MEMTOFT0RSI/)N, iie eitcsst. iniUcrm 



%.^'- 



fiV 



.;>-*,«i-4%.»' 



%2i6 SHEARiNd 35 

I^ u^exx>^^^da^4i<i POLAR MOMENT OF INERTIA of 

tiiA ciMt »e<dic!n , a Ls cussed lu | L|i| •, e U iit rcJdoJi ctrsiaivt* o[ 
Tiie ourertuou eWmcrit^ Arid =: !K& ra.<^«ui joK ct ^ii^tular slic^fft, 
•2l7. TORSIONAL STlfP^^bSS. lrv}:>roWemsm- 
volvvna ft»€ oin^)e ©f tor sim^^ or deform oKon of rlje shd-fljyve 
rieec( au €(^(1(1^1011 cctiiiecttna Fa a^xioc , v^'hidfi b cpfeniei ki 
sub^4lMin<3 u\ c<j. (^1) -i|i€ value of b^ n\ e<j. (.^j^wUriefi 

J2/S. TORStONAL RESILIENCE hi-L Wr^U^\^Uii- 
ti iv\ w oictttYn-o^i eleiiien+$ . lUw |ta.il3 we hi^i^e Hit riafcf'- 

twU'iedl ^:lfurou<xK 6m aiwjU o<i ea^li |ott(>. P "ctjlie csu-j^k inu5+W 
moie 4t> ivic»eo4€ atftAife^tl^ Iram ^l 2€n> H<m^i \A+o iie valae Jl 
caTTes tenia h 14 it> (x^ . i^x ms mofioit eaeh endL^tille einna (ie»- 
crlbes a ^l^oce =*j- aoi« j smd 4ke mean Vfl^ttve oJ^Hu |jtte ~^I^ 
(s« §1]}. HeuceTke \N0^k ^Mm \ti4«(iiilnfl is 

U.= i-?»Xi-a«,X2=|P,ak (5-) 

Bv Utt ai<j[ of pr€cc(iiiic| fjJKaiimis /5] c«xn i^ wtl (fen. 

Ij -for |j wi wtU^ S'' (_M5(!fttil« o-f «a4 ^-ii^aurUi^) vv£ Ure |ar 
{kie rest Uc^icc of ike sJta^. ^^.i^p t 

a| aire»^:ii»uj iU >ii.oiloii of otttMW^hu^ m^ts wfiDie wewijjii- u fi, we 



I 



%2i8 3H£ARmA 64 

-2^. POLAR mmEMTijf mBRJih. For ^Ji^|f ofm^ 

\i%(Ltt I^ -J ^t^^-^tyi wiife 'j^rd ^(|3s^si« Jwf Jf-~^^, 
% fcecna ft^ v!i«. 6^ fee siHfc4?«;^Tett"a?^^ a-i&ss-^Serl^ 

^^0. W)f^-C/RO^L^R SHAFTS, I^ lie cri^-s^^Wis 

o^Uh'iaiti niv^sfiiMtiloti^ e^Stv^umd Lwa^ efv^ majw i>j{i«$€ 
ca^s, (See § /D2 1/ Tiiiim|»$£?n WT^^tI ^ith^l Htteo^y;ftb- 

and Pa :=^t>^i3^ /(iwl^cui «>f ^/C^) «^ %2l6^ p^ hem iktc^td- 
TUt ^em^rih o^aTtttfrc^ s Wni^ $jxax% (m^ -loiaui at the 

uni^nni^lNj ai*^ overcame ou^duiifcate Cl^ ^jif, j?reuuj6 $4- Ha 

^ PcL 35^^b . (Pt flwi 6» +^e bearltfvG r<A^-HoKs li<u« no mow- 
twTtttwvt "Hu o^u of fke sli/x|f^) Ijffte skix|f wUcg^ vt ni^^- 



^^' 



< 



.^ 



\ 



\ 



\ 






V 



\ 




S^^fc SAf£AR/r44. TOR^L^A/ - 51 

gy,|ggW^e( tu "(wfs^t^^ tN. ^U^tf wkc5^ dsWt Cr-^itJTi^toxrttiW^Ha 

How \ii 4iie S4ttiuLii.4^ M^i?^«^ -lie ji^ikwiWmcli ari-^ 

For -Hte ^|€f%i of -Ik sUff Pa iTutsf :=^ -^^4^ , ^om e^*<^3j, 
CL»u<i wift I^ ^=~inr* a*ki e^^r ,vtt Itdire |iHai^ , d<j{¥tuA |or t 

10 too Ur sW , aiid[ SOM for cAJ^^-irt^y^ . E4J.OJJ wU flien 




^^i. /icrm<i/?/\p/iic T&sr«H& machine, rite j^rmcr 

\n |i4. 2f 7, The 4e3+ Ucce t% ol a.«i'(itWAx(itlML|>c aw^ nre, 

(ifcKnt. h ciTflJLiMxlbj dli?iria4&d more a^ tuore 4toitv He veHliwi, 
pi^e lUs i-K "fa<,o^^ oi- mallm . ThU m^^rloiv o|- Ike pi?it<ii*[u)n 



*9 



^ ^oa) value of 




^ ^ * 1 08« *^ " set 







^* Force b1«ne *^ 



r 








,.^ 






$ 




§ 9.2X TORS i OK! J58 

viol u7n etjU'O^'to tW^ ?^ ^-C l^^ni^^^ufjf*^ an4 iKis ^^Vcxl. <iis • 

?T«>rF»eT»t (^, \ixrs%m ., (Xs me ^We Wjst;-^ five dTum m^d ha- 
per move unier the |>etipnl |W^^<<^h av\ mi^k c^ucxi t Ui^a*?- 

iihe Curve tH«5 T»w!B»4<^-i5rr -^^ ^x^^er, iy(-«*xi>ujre ^*«ki£H %t ^^' 
siou:^£5 (rf 'frtc fer^^on , f*^, X? O shows H||>^Val ^^rveS 

ii25. EAAMpieS )NTof?5)0K TUmed^k../ 

S<4<^ :>Wmny ^creucfii. ^' ^ <X5 i^K^h m § 2ii 1 ,^ is e>c- 
*br^i^5^ \k^ ^yoyiX^% \^9 %€tujxrt Vn^iX 5 )i^nce lKes€^ two tc- 

Cft-vijii^.^ wncvc ofTe <5\ ttui aW^v^fi values tc}T S 45 «-cse?l. 

EXAMPLE I. ff 216. Witk ?..^ I W,^a-3fh 
X s ^^ f^*;, a*^4 the -roAius d^ %t ^lioWcal sWft r - 

5^»tH€K > ms sK^ft bekWj (jf wro*t iron. 

s«jr V it^^K wWtck IS <»> safe \f<x\u,t |<?v" <mv^ 'jeiVoas met - 



%il35 TORSION^ 371 

WAitJ^ .^ if il maUes 6*0 T^valulic^as ]>er pninute ? Let 
ttumbev df unvts of w^rk W urut d{ hme o>a$ttlut^n<^ ond 

' H.R -^Z0m'%,60)<JiTr X 3 - 33^(30 = 5/^ H.P. 




,ntf, TH.e srraihs mid* sa*tr»ti!i<Xi«.riw (jo^sTOia. fnja. 



^/lis^ '^ovdi \?n^ ciiOid a.x3(i#*ireiu j^^ i?iii('sTil( sdL|e.) 






£)Si^Bi 



l^QD H. 



ana rmtte 6t) rey. |3<?r imnuf e, f^ |n<xictir«t>n 



£)^mb(^ S*, In ^.?^mye ^» k - Z<\SO dfn.j^r $<|*uwe Iiic/ij 










%le^iiX^ dr<2fit OK Due df tie-^ise^^Le.^ —.2^30 ih$. her 

, St7ju(£!ir U in ike IsUti^ AC mil h^ ix^mxei a co^j;^tt%m 
tiv'Cs? o| 2.0 St) its. ber^^iH. I-f a bkWsu.t|du^. Wd k^n 
€x|7o^€cf TRA Ki%^ a-io* otK^^ o^alt irif^u i(^ wiiit^H^t lo^e «{• 

nor <i<?^^ csiiw v , , -. 

aU &K ^^*^ yiiift i^ iMr($ b a Uu^ ^^ie^^ti^ilc^ or o|-<ymiWsr- 

CHARJE. 

FiejMtre £?t jtf^n£>^u«^^8U Prisma uW«r ter bekuuc- 
^(ixr hr^A^ lu ®ne blasts - 
-2-?^./^SSiiMPTMMS f)FTN-E a)f^MO« THEORY 
OF FLEXURE. T/u'€ ii<u5Ty issfetf^e^ikje?tcuc4-f«^ 

ate fctft|>fetlv Ji^iovdn^d, c^ ^kmdf^^n^^ ^f ^i^WTimeic|-s^W 



arc ait fotfcvtfs^r^or i}»bfTi% ctnj ^Tui\i^ tii^k vertdWt ch^sj 

i^arcia ccc^i+rai st^rciJuslit Ojtb^vi^^*: 

(/.) Th^ cxicnidl (?T^j}lie/"/(?rAes ore ali ja^rknittaiarii} 
tk£ au^ £)^ i4£ |jt^2c« audi (ie in. &vjt ^io^u^ ^ci )ii«^^ he, ooJM 
Hit fijrce-jb/aiie 3 ikt jatte-j^am/t conial'ns Ae axis &{ iU ^im 
d^d cuis eojth crns^ '^cticn cfii^rrm<^fri«*llv; 

(fijTk^rt U a^siirfoLde w|ii^ t9 ^rciKci io 4ie. aicU ax<i( 
jJc-TJ^tiPidiCc^clat iT>m^ |^<'ce-|)ldK^ mtdt &hn£^ wilck iiieelc- 
-meiiis 6| H^ dolU e?ej?en€viee tio tension. Tior eem^v«Aa\©n 

t^ aTK oujclai cllte^iioii^ ^s teUa called ii« W£tfTRAL 

SURFACE; . ' ^ 

Uiiu| caty 4t HEUTRAL LIME or ELASTIC C(//?VE, 
ii^ ttn^Ucf or ^€)cttre ^t fie jnece U so aliafcf ^fia^- ati ein- 
menro^rv dllvl^ on , oU , i^ me iiett.fr(?Ll (liit woiv t« |?u^- 

44^%Leaiv<tt ^AArfjki^ are^ie Tcabeciive |i/El/T/?AL AX- 
ES cl fhi ^ecUoiu, exj^ene-'uee eioxiiajions {(rr <«^>tfwLc- 
nous^ aecc^<iiiu| ^« fitev are sifiattfli on. »^e st^ or ni 

amouants arc |?irob^fl«>ia.(it^iMi«ir^UWe^ Acm ilit litw- 

(7J TTie (/imcn^i ctts o^- TlIU crt^ ^teflon are ^mali c^w- 
jjAnd' wtfk fiK, ki^tL c^tke hl^e; 

[8) Tktre h VLO'sli^ar berpWtcwar'faiic ^rc« jjiUnt en 
iVfetiuxt ^ar^ces jpferibcuciiaLiaf'ib™^*" pane 



• ♦ 

fi^.^n %1U To far. ^.^2. §§a26-«53 

cf A 



i::!i"«^., 



>t— %. 



fc * •• 



i^ 



I I* • 



<V«^ A ^ /| All 






T 



* f 



T-TF 



I f 



/•S 



F;<^,^n 




^^^'' F-. 223 ^ §23) , 



rT' 

#• 






iW 



R^.52S' 






V ^' 




/ 



J § 333, 






f^l^.Z2$ § 3 33 



§ 22 f TieX I' RE -f 2 

In me local Uy v^^Vicrs an^ one at ftte exl^tnal forces t^ 
abV^iCA^ , ]6QaX Presses are 4 coui^se m<?»uxe<l whscK (demand 

226, ILLUSTRATIOK. Coi^s^ae.- Hie case of 

\lexivfe sncvw\-v-ii» Fi^. 22 f. TKe exTernsU ^(^rcc<, Are fliv^e 
Wstic curve, NA IS tK® newlr^^ axVs 4 S^*^ cyis^j-scctionoil 

.; 4rawa <3tt the \ritcr;sect*oti lines* ^ clfier v%ft^4.S^lK8 Sids vias/ 

line . lo Cons {dcrln^ \k«. wW*!^ |3ris«n ^t-ee wQ^l%a^ I^E Sjs- 
T<rrt '^^ ^ J ord T m «^vL\1ir{ttm^ wVtcnce {r^sv*^ 2^^ 
vy« 'K<jye '[p =. "P 4~ T^ ^ a«4 -fvoivi "S^C^o^. ak^ilto) 
2= O'^l^l 5::Fl . Hence <?$veri "P w« m^av ieTerm^ne me 
filne^ }wo externa! jcrceS , A reaclicii sacK o^ 7 i& $5me- 
tunes caded ct s«i>^^r{ib^ 'farce. I he dements atje^e 

226. THE ELASTIC FORCES, d^meivel^l^ 

vn n<^. 2-21 sejpajraTed irJij iwo lao^rts ^>^^ on^ Tv-ans verse s^^ 
ton S««H as <3,A ,and ike ]xjT[fc:Ti N OM, cc^nsldered as a. 
frecbc% in ftj. 2 22. Of tKiS ^rce "b^aj tt^ sur|ac£^ 
QA8 ft ^wc» of &\e ladiAadm^ SuYfaces ^ t**!- w<a.& ot^^^tw^lly^H 
iito^irwl ^£({g£& o^ IW U«<J%m m F»V ^^1 - Hence m fc*2^1 
We wfli&t ]>ut tfi Bi^ d»CS5<t5 curtiivj <5y^ cdl iSie dF^j or ele- 

AdAmS ^ tt^C Voa^ lUkferv Awoy ^>ain iKe "iiiidlT^ wWK iiifcffc, 
onci cccor^iHij to fiLSS*tfn ^IioiftS (Sj >(^3 <3tv«| (ftj <^fi*^^ 
«f normal sTreises (^t<m*iw3n cr^ crrp\»r€^$ii>n3 "l?roWoifTio*«c4 

^^ lUintval a*is.^ finijjf i>/ 46rriTv:| sive^^cc JMhriUi^i lo- tk ff>vf^ 



§ 226 FlEXj/RE. , 43_ 




Tiitse theses ^ caljtd ikt EXkSTlC fdkCtS ^f ik cm^ 
^eciio^ e%\2c^td a^^tht exittmal -P^re^i P^ ^nd Pz j j^^^' ^ 

i^^7- TH^ NEUTRAL ^XIS CONTAINS THE CEiT 
TRE OF aRAVlTY OF Tf^/t, CROS^^SECTmi Fif2ZZ. 
Lei C' - ikt diiiaYj^ o|4iie oul-etm^d ei^meri «|^ t4€ erc?.s- see- 

are«3L ujjoa i^V be :::^^ t^^d1i€r Tensiou D^r compe^sicn. Tktn L 






T/iis c^iWiiTii Is frwe lor iF\ k^niW n^cdivt z^s^ut- on 



t'L^u^^^s J one ab(j\f€^ lie oiW b^UN*^* tU "HaclWl ^\a|3u>2, 
str^-^s^ tTa<lMXiu^4WeUuaaiior^aTe^i^« same. ^^»ovtd«^ 

Fgt I!us -We Di^di'j m (^lllhhim bixt 2.X^-0^^t3 ah^t- 

■/f ].aF ^di U|]ir. -fl;cr,lF£ -0 -- C^) 

in wd'tck ^ ---. dic.hxuc« of fjue centra o^ <n(XM\'^ of tIu c-ra^s-sec- 

xWa 5 ine ^^'^ kaA.'« bee n "jn^tujei ; (liea M^l^i) § 2 SJ * 

Ik ^t^] nctilier |) 4 e nof F cah ae zero •* . z tiia^i = 0; 



i.e. iiW utUfeirai a;^H eo^tais.^ ikg (ieatra $| <|m^dv. Q.E,B' 

22B, THE SHEAR. TW ^Hokl ^W% 0t .Imf^l^ iU^lia^ 
tn^tke CT5^$-gecii$?i UH,e sum e!|-ik.H€ftkisl^W^~ii^ &WtS£5^ 

Tii^"^ ts^'i'k^ skear GjH^-s lie a(.2^tme ^iim of "fie o^eTndi |&f- 

lu-tt imbiifs fvoikiiid c^i^se^^tfia a^ m^-t 0^ iiWiftbrfisii ^fTifie see- 
fen. 

22^. THE MMSrr. Byik''ti^-mn^i^cj tUr^'',cruv^ 
s cresses <xr^reai aiou^-f ^n^ sK€^f W<iiu| He tef^ Wt'^ M fe»f^ 

tau ^u^iu^i cay MflmEi^i df mERxiA u. isiyro^ 

TitKWl a^i^ H^J -=^0j W€ futveiira 

eoHiidefei , viitfi^sue oi-fke ela^'tc l^xCes at tSi^^ e?L|>oteci S^- 
25^. STRENGTH IN FLEXURE, £^^.(5j is amUbU 



§250 FLBKURE- AS 

I%iL€ axact ^l tilt ferc^eut ciiA^^fer, \ij\ittz all H^t Citteyiud 

ffcaT Hn i;oTti4^», ^W^^ts im. ouh ^txiltyi , a-^ QB rl % 212, arc c- 

Thc&€ -iwcf <^i 0.^ ^r<ti{elvt.:i4»ikjik, n<?^ ^dn^' kit fk $aine Jbt, 

4iA.rikir e^i/oit t^^i^t^ retSiijiiMd, ^ce$ tit jta, 212 ^}ii:L.: iL 
sW-f Jpx-jv^ tkt, <gf"(f rnsA |efe€C ^ q aiwt P^^ ib^ e|iuWe«d ^ 

2SL FLBXmAL STIFFKESS. Tk ii,caW (iue^oreUiic 
curve, ctfuioWWiA^ cn^Tci^ o|- <»^^ck 4)^ m tk« ^eisfems, vtos 

luL JW^ <£i4mtij ^utfi masj W. lifrfia^ <2i*& loiWs , ^S oufui 

-Htc Citier ftbre. But He r^t^rtiVt etcK^safion £ -A^ ^f 
From ^j Ou raL(iias5 ot Cuyv^sikr^ 6iii Oe c<?mj?tae^(. E^iji^ 



lu^. 



§2^1 FLELX^RE 44 

To 






lo «xi£|\ ds- <ii"ii3. -ig^f ^liirfmW^ j:^-om!^ <^-.s«sy*ed^P3€ {; 15 {i- 



8 _ ct^^ 



03*4 fiencc |rsii6. €^. {^) w« We 



Kgmo^a%u?>c5 twjfi E (Htt(i I at€ -Hit sam« /IcepnsWf) ai4 
WniV »|H^ e^^tle ewxir<. J^ i^^ma /7)ikea?4^Xm»5^^ 

nittsi fcettto/ff. 
2^-2. RESILIEHCE OF FlEXU/?£. If fieeKfernal^^ 

|)oini^ el ojjbllmH^u movhs^ tkvdttak oerfeuH tiUWc^ du« ioi^^ 

rk^ ea^ 0^ imtt jfctdijUn iit« IxJh U aired ^ iiis wW' W btenef^ 
jpendei tJU tke elis4ic rt^isicusc^ o| 4ie bci^ cui^ an ^^^ ^' 




§§l^£,i 



§333 ELA STIC CORVES. ^ 

ELASTIC CURyES. 

233. CASE I. mKlZ£)HTAl PRISM/KTIC BEAW, 

Si/PPDRTED AT BOTH ENDS, WITH A CENTRAL 

LOAD. WEjei^T Of BEAM HE&IBCTZU. Fi^ZZA. 

Flrti C07xs\(i^\nn fU wkoU team tWe^we -^an{ edclt re^c^^it 

(?f ffic ^erii«L OB TtrUfFx%JL'J:o C OS €m ^^In a^A-icjU W- 
iiWt ttue "ikro«uflit xtsilteojtVs o|X^ To do ^^fus c*nttdi?^(ss 

fcixiv fK e^uIUSnlum ore Ku cue exierTwii -force y^i^^ ^^* 
tiic ?i€urhrut ojt m of "m , o^ <ot of is <>| r?l^^HenTS ^ikai' Jrm.\^ 

ucjHiiCj iii£ WHja. of oc ^ tie %Up.^ or oa^U t^tw€€Hl{tc'UK«^«wt- 
EIX^-O-^^C 



§2 55 EL /^STfCCUmES ^4^ 

vrffucfi eyuibU^ ca4c clefts mW ii%t (^n<dxD^^ C, vy4^S€ v^ue -mast 

be flu ^o-'uie cd" o^-f^-^r oil bouii^ ef tii^ ciiS-u^-. Hence C=^<? 



""'-TS EI 



eow^iion offk^ eid^^iitf carve OB U t3 ^i t ^^x 

^ ^ t-Ii = ^(^-i/)-.C3) 

To c^mfcuic+kc ditledlm e{ •^m+k^ dalii tine ]oinlH«| A 

U^tsj oi jifl. 125" eyte;>iJ^4oT!i« left c^ 0,iit« oy^^iW |o»e«5 

of 1^ Uiier abiw J iiLus alfaiKfl ^e -tcmn oj et,0). Ftottl s^m- 

yizoX Vtl^kOB oiou.'HKe veriical 4kr^wA U. 
;233,a. LOAD SUDDHNLY /APPLIED. f^.^^Jotvcs 

Utcdl (XT -fli^. YtvUliU i)| rke beam a^Use€'n^T>W bro|toT'fioual 
lAuhtid team^is suiiexl^ veieose^i -froratli^ fi'^ieiW.c^u*^ 



ll 








^2=kr:' *S-^'^'f 1 






1 
^ ft36, 



I ^ . 




^?==^ 










•■ i S 



? -////////^^ 




<«..» 5)t.. .■..> 



33 



% 5V0 



S? i 



AiArfYai-^ li lt % . 4 ' M t 



^i^r<»m 



SJ2?3a ELASTIC CURVES. ±^ 

=:t!«-^ bresssu^ bfiiwftCH Mks toad <a>idl tU bemn d^i\i£ iits^t»^o| 
vvKvU lis kmiW (Tsvl filial kinttit €n^<iies a^t ijotit TioikUa. 

i{\\) If itnm^edlitfiei^ U<ntts ox Miwori mcjlifln reackiiw 4k€ |?otnt 
iiefc 3ap^€ ike dltt4w^ (ft w beatn ttnhaWrred . TdW b catiW 

I^U^, andi <]LdLo<i.btt de^^i£kis>n* TU ^<>Ti( ioue b^ B*ebe(3iY»i.iU 
Slnilii?j/^, (| m wei^i 4 ts ^lUcwti -fcM oniit midk^^ 

J23^. CAS€ir. HDR120NT71L PR1SiVlAT7C SEAM, 
SUPPORTED ATS^THENDS, BEARiNfi A SIMOLE 
Et^CENTRlC LOAD. WEtfiHT OF BEAM NeaiECTED. 
Fi^ 557. TU reod-Jon^ (^ >Hie [)ohiF$ of ^up^c^ft^T? and R, 
art e<)^>iij -ftvH^ ^ o^m^l^^WA ii^ wu^lf bfiA 

S (>iW)e =rO, wUe^ ]^ - Fl, ^(l-U) . H o^^A p. villi 

T/ve dAslic caryts OC omoI CB , +li^ouiC|li Kavrna a common 




FLASTi€CURVE.&. 5D 

iouAtteia ImQ cd (3^h«( k%vLce 'xIul some ^IpJ^ ac^Jfani aionwwn 
ofdincd^ <*^ C, Wc debaya:kt ejiA^ww^ mul osrc l<r{i. Te'(&W4o 
ttc s<xm€ orlch^ ftjui axe^, as ^tujwx luike ^coltc* Tke s/ftkdf 
0, ot^ J OAfui rttff (rf* B, «*., ^ ar<L iMikKeiwTi eortcWsjifo Ih da- 

BQUfiiTlOH Of Ofif. (Lm^woUW^ as ^n« ^foiHWx frfi4i« 

$«45^i«rtt, W( conc^vr U« ciasjile -farcer |>idu.«niU €*tJ3o>«rf 
tVL^hx^^as iTtL ike brt^^rflua brtctem, andt |wct Sl{wmi. a- 

To ^lud C , wrifr ^ +kis e^jtia^-UK -f cr ikshchd'O^wlitn 

(^)^ aixct (3) n o v^w-* ^f x Ui© b< U4i^ <0 or > 1, , since 

kaUhVlOH ores. ^1^.227. Uf^^freeUdvj c^- 
"^^TAa -fn?^ww Bio a 5«^lt>nTiiaa(tf aivMVrK«t* ox 06. JS^noms) 

(N.B In (^},a* i-nO), Eld'-i "^^"^ i* w^''^^**^ «4uai^A 
ucaoCrive <{M<i'n+i'K| btcoase lt$fcl^e»?«»vil4U.M ?i«aa4ivc;|^ 



§334- FLEXURE. ELAST. CURVES i/ 



tat cuwe i*f eonCAv-'e U ^c ax^s JC in tlie jirsi ^juach^nt of 

the co^ordttioTc oxesV 

Trom (^t) We Vi«ve tri H>c ordinavy vaw ()C omti^derW/) 

io <^etcYirnoe C ^ consider tkcrf. Itie Curves CB a^4 OC 

Wve rt^e some ^lobe (^^-f ^vj ^t" C? wl^ve ^- I ', }*i<rvie€ 
jstjit 5(^\. 5n mt r«^t-Vusiia^ -members of (^2) a*w.^ ojCcV)"^ 

(X{ C ^v^Kcve x=: i , ^otti curvet Kcive IKe same wniirKire^ 
>\€vue^ \y jDuUjng X =: I In tke -^^ koruJ rrie^nWrs of (.Sj <i^ (^X 
oirui e({u<itmg results^ re cbmm C*** = — ^ Pl^, -.(63^ ^' 

'-'^^EIy=:tPr>c.EI.^.-f?[l^^_|^]-^^ (6) 

as rtic EQliATtON OF CB,B^.2il7. ^cvi; oc,/v5 stai anuR^ 
IcnovJn <rcn&Jantjtft -jipd wWK wrtU out (6) -^ 4»e ^wrnit 2 

^»- sin [^^ ~ 3Pin+^?.l'J.,,..<7) 
^ 235. MAXIMUM ^j^fL£cV^oK^C/^SF]I;^f 

ftj, 2 57„ TKe ordinate tj^ of Htc West l^oint is tiius f?^d: 
Assuimn^ I >-j-l ^a^ Wi ^cc«.r tti{{i< (Sitrvc OC H^^w^M 

f'JT oL^ WTt+e in value A^ »ri (^7} ^ Uvm^i i^u^t H ^ Pi -f Z, 1 <**^ 



§?3^ fl^gjXURE, EiASTiC CURVES. 6'2 

wW. ^^ ^„, -*-y ]- v'tuJirO Now ..ut.-- 

lute this value 4 X »«C6), <*^^* ot, f*^- (V) jfl^'^ ^^T^^y.lH^.^ 

236XASEm. HORIZOHTAL PRiSmTlCBEAM 
SUPPORTED AT BOTH ENDS 4ND B^ARtUa A UNt- 
FORMLY D/BrRfSrrEU tMD/4L0Nfi JTS syHOLt 

Anot v^r-fiie wi^k+ , b« aiiii j^| (a^fk^ e|-+ia (odflihw ,• fW -fitc 
it/ad c<muivt^ ijoon (x^u cewjtfv x wia t« ^ WX, ^rU w ^koU W 
^wi . By ^jxjft®^^ V^ Is c^sWf . fic^>2jB. From t^rmm^ipj 

m.toW(e ^1' 4^t« yitsL^al (in* U lis i4>we$"^ Ui^i, a^^ ik* m^ejii 

tortloK ^f be^Ui mt4{n? tkikf ^|! ^nit n^« ^rees [toUHio iluvi pax- 
fioTt tu G^tvlti^iflani oare -^ wi | i4« res^lkri at 8^ fit efosfic 

laiffji' tcra^ am^ m 




X (i7i«nt. ai©<^r '^uiiiTa/ ot^U oi m) :=:0 -fe^ ikl% \reB W^ , yv« 



.^236 n-E%URE.ELA.^Tie CUR)IBS. 53 

di}f-(ix caul K dri^ ~^0 ^^«^''« C^)? 



^M ike. Cttrves isf Ccwe^ I cW lEj wWe iher-e were tu> cddwi- 



ill*. rioTiJtou'Ui tb^?Wi A audi S, Vi^i^: O^^'^^^WIi^WvWj^ r:\wp 

32* El "'^8^ El ^^ 

wli^t only ^/>jiK?rt- c4?Tt$is-fe in <ffi^; W ielua kiiil U (^vt^jf, 

6^ P fij ttiAl e^^itifiTi, i4e reagiUn at Q m |i<|, -230. m% as- 
sumes H^i the TH^, c[£|/ec:fi(rR i^cears |>€+wfm Aoni 






?i25 7 FIEXU I? E. LU^^TiC CURVES, 54 

ixUc po^e 4W ^|i€ (kp.ecil^fi oi bwwike iaii^eni ai U 

238, CASEY. HdRUOHTMPRlSMPiVC BBA})fl 
BEMilUa E&UALTERt^lNALLDAOS /IND Sl/PPORT- 
£D SYMMETRICALLY AT TWO POINTS- Fi^.t^L 
WeJ(^!if of beam iieA^cciW. Jnii^ ^rec^^c^ coj^ei; wc Hav^ 
mctd'e «s€ d| ike 4.p^voxinux4e -form Eld^M -fcl>c^ lu^^rf*^ 

Ht«, more e^^acl e^- f)Ye?^ ^tMi £1* -rp /see §^3/) -ftr\u\nm^ 

art ea5Ji -Vy -frofty. suwirlefry. CovtViieniM -/rc^ d^vti^utH^tk 
pc^MA. e^VidlHij -from A fo ax^ ^et^tcat m J^^fw^n «jtet C 
(fi(^, 232y lA/e fidi^^iP, by |juift\ui 2 (m^fl^^. abou+ tie^irai o^U^^ 



S/^FF LMDS m FLEXURE. 

StiCrioM ei" aaSirsfi fcsawt fW.er a^jrea /oftcfnu v** liw^aiffo- 

In wilt fill I IS i-nt *^Mor««j5f (J^ XneritV^/§^ir) (?^fk hhsmt ff 
W?e ol ii^4 •rno^t ciUU^if^cf ^ufer) ^illi»«' /roiu iii«t ii^tital 



cl OiY ikt -forces oi^ffncj ch ilie tne ^od^ ot w\tkk Met seeiiotin 
meicfs c-f-Ti^ -^^rces w!Uon b^ionc^ f^ s+rei^^e^ c-ltteseei'l^Ti, 

/4^ aara/^M^oI re^^seni^i^ii (r^if!i£VAtfciC^ c^ M aieuaifee kea^m 

"kcAt {)Tc(kuiiieft (^C3u£a7r(it>w3r iv senate it|mt^ ^ caiie) '^ron^ a horuon" 
m ^t"^ |wsii Mow T\K Wo.in . If tte u|>|>er -ribr^* a^t^- W m)^- 

Yice^vcY^i^ jor lib endeiik- {liid d (xt^tdhiL \^(m^U^O A <ih^ 

It \S okl^o ^idewir |rc?TA *|.ii) S^3/ ^iCf ii^ ttxAm o-j ctorv^LkcK' 

EWr Dl^&RAM , aU fWlr^^^nlf^^ a MOMENT C(/We. 

l5f<f{to%'\v'iie?< M -S^iy^ , Zf^jkal. iooLtoLU y«U^ R^ AAflt iiw^ n«w( 



Eg, (2) ts otVcxAabie |cr ixniina A^^/ one ankncW" quanli- 
t\ijV\lWlner it b€ d load ^ Sjxan cr seme one (Atmension «f 

STf?ElVQ"TH» «^ »«t Wvik IKe. st»^n€-.5 cf iKe beam. I^ 

ck^bk^^\%A wt(( t^ ^.m-ii "io be uece^*5-»,7v im^ i\ Wins c<?i?ij?o^ 
i>(-{X'iklll Wife UUiini*^ %'i; -f/aH^^, T/i« jpiaf j/jji^t/ZoW'ey^r'yek- 

2J/4>. THe SH-SAR IS THE RftST x^DEKIVATIVE 
^F THE ftl/:)MFNT, Fi^.JL2^3 C^h^^dkioci^ ofan^ «e<t- 
Ttcvi, tgi€^3 uxM fxxxaiid fo f(i9 hmiii ^ -tram. OK ^jrilfrajr^ 0fu|hi) 
C^-xskkr CL^ fc^^' '^^^"^"^^^^ ^'^^"^'^ c-f4i<'^. |>ea?^. ■ lvu*iadtea pd- 

luHftf (aii koA ^omA^ boTiL^ J ^Dmi Ion, wix j 5| 'fei l^ac&n^, 
wid-ck a^H4h ^^t?| 4^e ht-nm ik^$ some rkt^?maK- •:?. w tb;^ focr 
rufmini> iiOi^i^' umr . PuUi^ 2lfi^u>sn. a-ki^aWn fl"^) -C wt 

But- ^-^M.ika Mtn^6^ o{ #,,, Uff h&%d s^eW , -^ rr M', 
tor \H ^ Y&aai\t^ wit€^&dd^ i^ihL.--fi^ Tli4*3 broY«4U 



§2^0 FLEXURB. SAFE WADS , 57 

7~1uj sit^ar- X <i^a)tv ^cxifcsn Ue^i!;i deifznniyi^d h\j c:im%<i&^ 
iw^ |V^ iU bcrUcH e| t€a>c iroTrt M^& sediiw tc dl^ W c^| t^ 
bedim, AH<^ :u4iffH^ 2- (verncd/ ccmbonenit^—C^ 

i*i.Hi»« ^ami ten^i, as Vx cs/cicfu^it.^. cimhiucaiLf i^k&j a^rt ilu^^^" 

rive 15^ cf "sevise p'v't "siisfeai nef^r wtesi ikt u^^m h dill i^Ts^- 

dU^U , Tl'tU 19 W«1~sfu)WH hj aiawjwj ai4^ al^m'^ , w/iose 
^fiil^wxits ,3,1 <? Uid. ojt- veiif coi/w tent <3i kotixi^rchd <^h oMd «aii- 

Ik +W$e ii^jurra-m^ ii.e 'mt7i^ei4' ^Wi7iaie.*«! are 3^ c# -c r* aw 

tiue^iT i%u:k />{ t>«pe«| im slums ^ Wve^ ti^p^ f^mt^^ oi sc)xe 
ctiitTr oixjt of fake, <?^ a iSoile ©| ;^7>^eiiY f^*^^^ l^tliei'^ci^ cf 
jaotLct . TK? %c£lU cnt willed, tU^ fcc^m i"^ dfa^n It'^oTsiom^ 4ef, 

Z^L SAFE tC^'/id .4TTHE IVI/ODIE 6F A Pmm- 
mt 3tAM SUPPORTED ATTHE EHnS. Fic^. 25^, 

Wrfinia Ufke Wobcr doj^kc a^ ^i4&ryu^ -fotc^. TKc w^V^ki 



WVHfljic B'Rft*. From wmwdi^^ , ay*<>mr Ww^jU C^?A' frri^ 
lite (^Hrtv M^ ^ fU.mown1 (sLfiijfa'm. Fram nit|>e4v8}B|+U 

(/Vi m«c) =-. M„, = J; Pi a; 

Aiplfi fcy jjut/tna ^ (vert ^ew^^cH^ -Cy^r t/ic At^ ioi^ n B 



weliaw'f 



J ^ ^ 



».e ^U^aif v4 (50usf<i3it <^\\d -4- ^ <xf<3w^«! tecfiou Ik^^ r\(^\A 
ht\%ja -jWe, +Tom 5; (v<ff.e*m4^0 , 

wAxd^^Uit^ --^ <xf 8 (xmJl J ai n mutf i^ac^tnc^ il^^dmn^fm^ 

2^2. SAFE lO^D UNir^RMtY DISTRIBUTED 
^10H(^ fii PRlShAATtC SEAM S(iPpC)f?TEP ,^T 
THE ENDS, L€:efk€ iW^j^i^Hea^lv^t^^fU^^ 



-1 . ^ t^ "^ 



.^^.^ . ...■♦••• 






*W"« wl ^. p P^ P. 











R, . ^37 % ^■'^^ 




F4'<t.23« 



T-Mv.n:;T«:' sa-^e 



o-f fU. ktocf^x ii^^if )' Fu«ii3^. Front ^yi^me+r^,€cui/i r^o^ 
koH ^-^ wL F<?T \k(i iv^^ fcotij rt 6 w€ /wi^c^batttiiiq SJ 

To ^(U^ ikz %\xtsL% TjcA n^ we y»a>/ elMet ^afx(v€ri 
ii^ same at i^e^^rK. 71) -fiW +i/e 'maijt.M^ oi M^ ^ |?ui J=^^ 

a4^c e^uarRoH of ^aje loadhCa. 

^\iiAi bccaiv. wli<r€ vve|iwi w iua^,IV1. 

rf ajVcci-ioKUs^ cidY«^aii j^itcf wiili vertical |dc«^ vve^^U- 
tr^ciuW od a\\u local i h luii^ beam miti iku$ (jUvl^Hlve 
lK<x%n ltiit> +W0 bdrU , flu i>rf^«YU« o| J wmaU be iii^uie iitOll- 

lite v^^ci l( U wen xM li^ ie^pf f^ vnUdi* . TU^ sicows wk^ iV 



§54-a FLEXWRE/SAFE LOADS; 66 ^ 

ortiitwslfis %V' iKe 1w<5 halves c[ ftie- sh&ar dJo^mm^ Kave c\>^ 

EauATlOM FOR SAFE kOADiNlQ. 5^. 236. Given 

tbfc iot34^ 'P , p 3,<Jna P^ ^wKise distances frorwr Itie yu^^t 
i^)^Qrt% cire I ,!« 9^^''^\':i 1 reqiiur£J the e<^cco<tion "for scrfe 

Co<^\ru<cuS' -furtctfcn of >C ^y^ts^vi evui fc end df tViC teain , \A/e 
cou\a casMy -[md 1/L^ '\>^j m^loM^ ^M ~r- Ax :=. ^ i.e. ^ 

■]or"Vl , ^ut \t» 1W trf^se^t Ca.se c^f iS^tacliecl XooAs^ J |4not2e- 
vo uecd^^orAt/, oX a»n</ secHon a^ IKe teatvi^ StiU iHerC ts Some 
one •seelicn wK^ye it cKcu^eS §4511^ i.€., k^x'isc^ Sui^evily 
tltY<?uc^)a lite valu£ xer<^, oindlKiS w'Al \>e tKe sedtion of t^reatest 

Wa ci^aal to THE REACr<ON AT O DIMiKilSHBD By 

TViH Loads occt'Rpt?^c B^rvvtHA/ n ^^vd o. Th^r^- 

Xl^ n uwen cai\|wif«vt belwten aJuiEj J"^T^ 
TI4U (oaf vaiue o| J Also :z:*f/i€ TtJ^tc^Un ^44e oiier suifccYtB. /^c- 
sliiAf flf(i^ra.H 5. (i>i(jt '^jcf •fcroL^ufiWrn (^ijein 4/tc^$S^ ''f t'fci ^^ 



!l 



§^4 ^ FLEX URC.S AFE LOADS. tfT^ 

n?e?u ctiH/c incrc h uL^fAdde^ e-W^e In fiV sneaf ^li^^j^tie, Mence 

! lis ' 

porKoii^ P.iiD W^tied iu h^am h mild hj ^fte [oah, (i?]iev edi^U&oi. 
lite ^(obg. 0-f "ii^. )TiO)ti?uiieu3fve and tit^ m;dlme of lite '^^o^^ 4a- 

c^twj 4t> ^ tt^(rkdu ai oii€ Drtl^ alha s^i^or!:^ willed €^€f klkc cmi^i 
a^d 4\W tn« 'Vuomcn r cd eSier ^Jilmf h zer©^ 



ibort 

for iU ts%<i iH|tor,^s4 we maw 'tit^^-fi^K :da:><i +Wf tk bv^w^^^^iuv 

hW &^ua|>* 5T £^e£tai five tf^\^ s| ii^t suj^|;*0/t, Tht ammw' 4 

cl-iite beam Ikk wluftii +ku ^^e^ti&niivu'U^i'iw bea\u 

^>^V7^ HiimRiCM EMMPLE OF TH-E PRECED/j^^ AS- 
n CLE . Rq. 237. fiim ?^ , Fi, Pa ^ eaiujii +0 f ~^^^* ? ^ ^-"^^^ ^ 



|^«i J I2 ~ 7 t''^^ ' a>^d I3 =: to M; wlili, 




W. Value cj K'^d^ 



^244 Fi^F'MJK E,SA fT. LOADS. 62 

fe)c|5T€'a* 0.11 foTo^ m4^)n0, wnife R'--^- (|on$ l^^r $<j.meh) a>\.jf Vu- 
if.yj^yg-t aU t^l^ife. ^ Im ^^vii^ ^ ^feu . M(?vn gills ¥rS. hi:hi hMm^ 

any ^4ie<55 e^bre-i-sedi ix [(>$,,. oi4dk«i, Kf sff.iuelt b 5miu«ncdCL |/^^ 
Mafe;u|ik£. v\;b!€ bf:dvru -free , we hds/e fj«i>» moms. alK'*<t 

1 he sneav anv'-^^Wvc belween ^*^^^^ t- '^ 3"^ 4" 3. 3 to^iSi 



jOvfS 



ti'H5TTient V, dt H^avjdi mdan^ HO ^[ree Was a vc>lue 
rn ^ 

tot <^a/^t> bouiU^ lis ^-- 









§24S FLE-^CURti^SAF^ LOADS. 65_ 

• (2)Tkt^<}L.U IcaA h j>vo|i«fKcnal 4uik s^uux^e oftke d(.i)?ili 
(3)TH€ safe /oa<i U t«)^<5rfen+D"l^€ ielj^ii d tedius (i(Mfirv£(iit« 
(If is KHder^jiW tJwtf HvesXi^^ ofliie seclicu axe fioni^feiii^ssJ a^dl 

2U(>. CCMPAIiATlVE STIFFNESS CF RECTM&UUkR 
Beams, T^yi^^iU (Ljl^ciion w^dexi^^ a'^an.m 

iiievct A it«.4ma" et "Hie ^e/cltow diou-f rb vietutdl oij^h , m vjit^y M^ 

(•2.) T/ue sfj'toie^*^ ^i^ btt)|>c^1 i<^Mi hMii e*^W c^^ Hie hticikt fo'r .Wfes 
bean^^ o|e^iiA( V«Uiu<> (|?|iij 

^t/A ■n48LE OF MCmPiT^ OF INERTIA. Tk«e^ 
"HuL (ii-fifaue^ o^-iilii i^i^.Ufy^fi' jtbt^ front ii^^ duy-ts. 
live s"Wtvis^'Hi \snr\n as X t e /^i b evidteni- i4idi-(i§<ji«tTe b&ami i?^ 



^ja. 



El£MB^ ^ AFB LOADS 



64 






ifrS 



.Section 






-H 









l^'J 






n 51 









:4l'^^ I \M 









^12 & 



24t UOmUT OF \HUiT\h OF I- 0t.4fr1S,8OX-fii«' 



M.CU-, sW>^.3^i^.$^wm 5|<u€Jr% v^ I 'fitter ^*^cfcms lia. ^4ndk^ be'i^l'k^^, 
€iSf um\i . 71^« I ^i-mi^ rtxm^ -^mu -^^^ ic aion^ IS' lutkat deA, 



,4* tr 



^a- ^8 flexure:. Safe Loads. ^ 

"be ewxmmed \<xter. For %c jsreSent llie )>o/t& areassuns- 
ed to act logetKe v as a conhauoas inass . For cxamlsle, Fi^, 
'f~'T\) shows a box-feiirder*', jorTiie<i of I'vw3'''^chomieis''' and 
Wo -pla+es fiveteti logeiiier. If %t ax'is ol s^i-nmetry,">J', 
, ig^""(ji — f-q=q^ islo-te Konzontol '(t "becomes tli6 netjlwt 



el ? 



a^ 



^^^.^^^ menttoned) otout line axis 5T Wrl>endiei^- 
'^^' iar To "ti-je web d5 Hie cKannel, I Hen ti^e 



F* 54-n ^^'^'^' nii)rnt-7i:t oj in^rtua of the axj?Tbii/7' 

H 

ln(0 ; ^^ ^ t-.^ iAnc^ i are tUe dJ^^lavKes ^^ven m rii< 24-9 
4i exlend » b Vhc.. rnxi^dle oj pldte'). \v]iv]e 3/ and f ave'tK^^ 

ienfjfli and vvsdlK oj a. -nvet ,, t\-\5 |t»rY^i tr |yovn l-\t!ad. U 
liectd ;; i.e., d'^cind t* are ttie dimetistonS of a rive I- holt,) 
\ or exam me., a boK-c^Tyxler^^t^ -jorm-e^ 6\ iwc iVmcu 

char.r»els c\"i-i«3 two ^aioies 10 'mcVies w/kle and 1 inck IVhcK^ 
Itve riv?!.. >ie]eS y^,, in. vv^ae and I %• ta. lon^V T?'v^1 B^ 

■\lS'-'^ -^^cm l\ir pocket *r20ck v>ie jtnd "iHc4". lor iKc cHann^l 






^ 194-S 



Abo, Since ui Ihis m^a«Kt e ^'- 8*j inAes^ end 12000 IW 
■ e^ so \tjch (cT 6 tijus '|3.ir ^:,\vv^ iS ftte Value -ferr 'R'' /' 3r..i:^Tseiii- 
•st s^t Twmval sWss i^m^ne calev tfement 0^ any cTt)s$-$€c\jon) 

~^ " as 

'i rtt\- «^, 5Ti'- iX)X'y\v'c5.'v .a\i 5<ivK; bear a ir-axmn^n^i m(>rr\f^A. 



F;^. a»0 wVt be f,»nri on >. 6S';»« Ihe text. 














P 



fi'.}, a^y, S a 6a 










V i'^^^^ 




F^ 2^i*-S «. § 5?6'? 



Un,l»<i4e<ii 



Pi^..!:i^6 



e 




§ a^3 



Fi^.R'/? 



..^^fcl 



FLFXURE. SAFE LOADS. 



66 



ik (.Mavlnis site«it6 iktk Mefii'n.auiA WiTt^rueJi, will W amihtti.^ 




1^ -{^io. U^i"W"^=^l "tou:m|oin\l:V clkWljtcieii «)il^i£ CiX^^iie^, 
o^iVt ^/muk^ bM -^^idkm^ i\D-f*^e WW*; buifi^xa XTA/ic^^^Pi^ih^ 



H..w«.-|^.«.' 









vvlVh oM^e«r - - It uuTIhjIj M4?<CP iiil (/?h|-. (tad 
^',Q-..y^'l :ri<f.^/-'5 iF^'.^a^/ ! 'K\j,i!3tj 



D-.-jf^'-^'feri 










■'■iJ^ii / 



W^v*'^M!fc!M^^^'''^ri 



( 



^so FLEXUHL, safe: lcad^. 6/ 



om i.aKf' 



*i>f4*J\| -fie ^r^QocHfj i?5a>(ey nniita e&b^eki/y t^ TtOTiye sto^IIj, ^Irj^jrp^^, 
a>ki sTv-(f litss uvvi^'t sw (udui, s-f 4toe Mi'n<e b^.?n, 

-|ud" '^ '^ict-? : w Weil's wtfti d4iv€iv (^^tdl ant-|ovvn[\^ Jt^inkWrk 






26~/,R^dc. F^C/R VARlCi^S Mt^rERlAlS. TAtjVmW.^ 










$m^t^ 'hfi^' 



I 



Tilt rfc'ilt^t**^-* i&bU •::uve< air«ixu|fe voUuiOi -^or R^ R^^KYsm^'E 
t^OM, e'ic4^€Ti^nav% tuf^^^^^j {3utii'S-^ii?6.-if^ 4ke^>j4e (U- EL.Wt^ 



^JU 



Pir;xlJRP. g.AF;:. Uaps. 



a 



cv:^ flie ^^^ya uirajn. boin\Ac 4f!*v^'rt»\ ctnci C^^mb^es^tCt-ix 



I niiD€r 



MiVf. -salt stress 



/OO^ 



7; 



.0-3- 



ncn 



6000 ixieK? 
110 00 ini/^ 



mc'i Iron 



12 000 



Sk-vt 



/6- COO 
io 

uoooo 



% 



ofirT^^ iV. oui«r fibre') 






000 
00 












J/COOO 



I] 000 



60 000 



JO 000 

liQdOO 



i J 00000c 



S^OOOCCC 



avekiui eTcfeKaio^i. c| 7—^ (;| one i?er teni., wfeil<> lU oorwfjir^s- 

rk T^LjcHve (Aav^€ ^^ i^r^ AWh) hum (iko dokhk. H^nca \ntm 
CAsi hen b€A-jn4, oH<:^ ' tdWt^ aW bar itcsyr oljHosf- Gniimi) <^ 
jpUcccl b«j relief WVTmA£j|it-ir»n h&Xim, an ^xm,omu oj- mehriai 
Was c'r|eeTd tw 'inixkHuj Hit Ciiikr-ftbit dh+fte cottibre<;s€c( 9t(i^ 

^•fe4W.-p.btt \H,i<iM<,i4*5.^ oMTijlii^ tH<*i)mbrmtmt jt.€-.^ % -^^,^hi 
a e-^m^Testiir^ si fain d^**-hk. H^Hu^iOh <u A? i^u/ n» ^eW- 



^M:,«.l favuMni*? a^v 



^l>.!i<Aai{y CC-mlv^ iUlt) l^e^ OlmJ Mi/Hy ulit];i«k'^« 



§ 2 5V FLEXU RE.SAFr Loads 6o_ 

Tfj^qrciX^ tanae 'jf ^fdii^ of H 4i^r"rtVW is d(ue t>ci chlw^f^^ 
^ifive AxcT "Hiit "Hve vavtous kii^os zrf irwo^ dilf^ wi<f« (^ iM^^i^iii, 

^Xt ot fit bciUH ty^if r <8jWmit«if has mucli rodo wim 4i^ w: 

of^ TcefijiOlCJoy i-Kli^if/ were -^hcuI^ onliJi su€ (umter/'SJjrU'C^^ 
iiii>Ui*^Du<s ^uekos axe tidu^dM 'fejceM Jet £(coy b Gains Ik hti- 
ay^ oave luuck ^VH^Kex vaWit e| f\ (yrcm 32 Od ic SjOO 

ba\A<c«w. 4U4vvo ^tA^lwr^s . 

mor^ Of (e^s broken ^ cfacks, K)ifii$,e;fc., tlie mcWr v<!tlti£s tf 

afain<ai, seiWferi |:^iec«, -frov* one-jocf 4c ^x-M lu (fncjiji 
N.X» Ircu audi Skel Co. ik c<rtaipufttiaUe s^x-fe /ood^ "fe ffeif 

(vviticli otre hia ii aiio cj^ m^tow wiCCTj TnitsT te s^ruare di|<Mii$i" 





' 2SZ, HmBRlCf^L EXAMPLES. 

U btwt iKb a c^(>«l4jr arc wkasi roM,\ji '^MO f(.7iie jiia^ i/[' 
bev\a fua bei^i^ j^MolUl ^s t!i£ sUt Cri Ttie^^i&kMt , Hef aired 'f^* offijJ- 

SOLUTION. F^§^230 diU23lmyyuxu^{e 



JJS2 F LEXUi?E-^4f :E Ujao s- 70 

For -t(*^ ttvuls [Htla and bc'tW (ylz,'~{kot'e. c^j^-'i'f^idbk m | 
25"^/) we (i Ave e -^ 4)1.,^ -^>^00 ut. ocA,A E ^2S' 000 000 

f - f m ^ ^ X^i"^^^^^^ -i-2^00 ^ 7 Biz. U}^ 

a^yovfe .b,j, t^^^^f/^'/^Xl'Tj tU^bers^.l'n^ §53^ sU^^ e^nm- 
^W'Ace yrhtr<t ft-koriUn, OC -[{V^St/t^ bfni m clcWcuUt arc 
EXAMPLE ^. A lio((cw <iyUivdfrleA{ Ofl-sf-ircH l>ik oirfti^ 

Uui -^0 kail o^ muei^^^^l /fe.^Jip^M miit7m«(i3(!€^tt3|^ 



±2.oA fLL^'^UkL SAt Jr L()AC)5. 21^ 

I )i ?.!^ i..tcl-'<r( Kctk ,j pi() T uiiv:^ Co. {lis ca(«^Y^ (i /^ mch 






;2d^^ ,*^ Stj^ 



'CS 



w(^.-:^ii Ij r..^ hcclic^ , N -20 A lo-Ki^ , ree^DH^wo end ^ufjj^a^s, 
i:j^<?^ b io cany ^a (o^ o^ \iOO tW. at f(<.€ uitddik ^ y*; (^Kirt(< 
Ht-t brobcr dfet^i L From § ^;«) 

' 7?'I , K' tii^ i-> 



* ♦ 



V&r 11i>^ s^^lctn (5f unit^^T*^ 0.60 tcns^'R'sr o.S'<5 Wkv 

<s4 ]x| liie ton^irion ihat the f^qkclien shall 1)^ -sr J/^O ^f 
the. ^p«n orlevjo-lii. "Wi $Kc>u^»i titen n«ve ^ro»>i § ?V0 

'' 600 ^ ^j^S "g"! iCSm^ file incU c^nd &n ,w»rif, 

E c: 1 ?0© ODD lU^ev sj.iiiclt^wVifcKr- 6oO tons >cv <.^ 
ineh ,j AK<i I— j^ Ts'K^^ we hkve 

EXAM Pii: 7. Pc«i*A<[V<!fa tUe levtjtk^f « wro'Ori?>i ]5ii>e s^l^- 

Vernal 2.60 Jvi.,I1H^I H^e deflection w^^i^^'r "tl^ ^}\^^*Sb.p ■'^'^^y 

fiXAmpU 8. f/'j, a^i". TKc w/o^) IS 6 feet Ux^'h ^.'Kd. 
**>^ forf 1li*€W , af CommoH. IritV work ("see % 73 «^ *^ ^0 ^^ 
"boTne l>v o« J* )>«a>vi W wliQSft <>uley ^»b>€S r»o ^>reorfe»' r-torrvia^ 
f^l^cSS IKfiit'^ 8 000 lljS, T>er 50 »Hck iS al1c?w<j4i)6. . J^Annm- 

^5 in. (^1^5 wK/J« iKc^ics),^ wKtcV one i^V\«]^ ^at eJi©sci% m tl>« 
rKc ^^^rv^fnt <jf meyti/i ©(the l^*mch tcciw^ htiric ftoO bt<^ucid[. 

'2ii3. SHPA-^iN-^q 5Tf?^SSi^S m SUs^FACF^ pARAIi.5^ 
To rHi^ Nfc'^JT r^.AL SURFACF. If cxV^^-s erf ^aavo^ (see 
l^Kj. ''4*V6j f^ used Tg »iuf:]>0Yt e4.]«a,ii^th6 l'>o«a>c5|^ V>ein^ jrf^e k 



f :<:s. 2Va 'co^S^ X-fc^e >.73 k^ 2a3 lo 55f>' 







Fi'g. a^8 %iS% 




H 



^J.'<3? 



F.55^? .5as3 



X./ax 



On un(i«y 












-5, F^. 5^5 





^[••.'V o.*-**^ 






%S£% FLEXURE. 5 HEAR IMG. 73_ 

1V»i5t«^K %t l?ocivds are df €cu.ai lehp^ij (^no^A' sec FiQ . ^^7); 

bin<:viton Ijemj no sfronoer lliavi tKe Same laoards iide Iw sic^e. 
lj,\>owever, Ihey qv-e glMed to<^€fl^ei- )j'ik<i as ih tli6 -fonn^r 
^tgMxve^-//i« tiiji^hi^ U bYei^cniecl and^H dctitciwn UvivlcJ) im% 
ixriderWxe sanoe l^ r. Thai it^ iie cJ\nj)oiO\(>^ fceoin h biSi 
<)^x^me< (x\U AlUe'i iiian4lie btl^ 0| ((>o&e boavc(i.s buf-t-fje tu^j- 

/;| ivteA \A/i{.{ vuw kf, cl€'k:i'\iui(«i bv i(i^' iteuotl'fviee'bodu mftho^. 
o^i Wciicn H\ d'P Ol brUniocHc beam ^Iwliitv bw undUrtom^ 



OK*/ Wciicn jV'. 6-f (X brUniocHc beam fjlwliitv b^vti" undUr fom^ 

xht,. 






\'^X'iub^ alcM^ 'tke aitiev sm^v-Iojc^g, o| "Hoi Uife^r, Ld ^ke wv 



&l^-_ __- FLEy^UFJE. 3H~EA(^m^_ 7^ 

W^M^ tUi2. e(i(?ax-iu(| t^rc6 cyx Urn u^U^^c suv-fcice h r^Xv^^^ix, 
q" k^M ifve JH'U^-cuiaC wiJiii o-^-iU kcan ai ikh <^UiaHce.^'' 
j-t6'Vii ikz itetcW am o-j^ N7 atu!( -ta^es ck Udet wilt? fkd^- 

.{^^,fj^c-a itiks tid^ -fekrs ^ "ixe dl^^it)ft(££ ^ ik.'?^^jdis.i| iiM* 
ii| jd|- 'fei ,Md |wn fdS lii^imTiM^-/ 

"■iiutCX "{usf f<Jt4Kj. . tit flu totv,;?.otvial seendfi wfecfi isci H:|^«^ 
SfiE:/v?i , ^V'llR T¥P VERTICAL CROSS fizCTimij Th, 



lft!> 



'^^^' gWe<^ |)6rfi OH y iyii^ above ^ii^ (c(*du(i^A| iH^i<^&t(^h^ t/->^ 



X-i'.*^ - SV/^OS f v^dlU JTaRci X ^1' (3ma5€ d^e -Hue, ^\t|v^ a§ 
For a^.o(t<y r<iemHau.((U ^'g^Iok ilka tt« (xbovcj ^ (^W z^ 







^^64 FL EX U R E . 3 he A R ^ N ^ - • 76 



\m\m^ ^\^[ii%ai{ a(A»|aec vv(ut< ii crosses |l^ vcriicftl secit^w ini^i^ 

c<?;u. (f<aiv. -Proii'. lf>ai <^xhj 



((oT beUvv\ 

,56^c5:V^/\Li;eS 6F2^ FOR SPBCML FORMS ^ OF 

dill 'ito? 



CROSS SECTION. Frout Hi^^ (o^lc^u^iioH H5h|?ld(ini^ 
fo+oJ 4(\ca\., aui hence ^o+lt^ avalW^ of f /ce 'sk'a^"^ d(i(Ujtram { r 

ob1:ij Uf J Ui fi<|5. 5 3>4 ~ i 37 hw<« ve , U ilwe ion ev) iciti , Ui U /c- 

pYo^«.r T^(aito)ia belwc^n +1ie IcAdlluA and +(tg |t)r)Ti a^^ niAikflo^^ o| 
i'li« b^'Wi +D secu^€ ^(t|ei\i auJAO^ftf '^ajji^tc bM jsi!€(3.n>u\. 

Tju- kb(^ lu § 5/0 fH^ &A.|€ values whidk -lU yiujuy^miuin J2^ iu 

iftot wdt; (8<?e fttjs. J238 ouic( ^<^) /tow^v^rjiddrt Z,q k (ikclv -io 
For ot (?£-CTANaLE w« U^, f o,5^"*3, (s^ ef, 5"^ § 2§/f) \-\ 

For a S^ixlD CIRCULAR s^ciitn j^.^d"// 
^ ^'^ 11/^ x^r^£r 2^1^ 3 ^r^ 






a Ho L LO VV CIRCULAR sec^^toxx {'coi^,<ii^^)ytc cyrc]e<) 







i-»»i. .\ 



-.1.1 -.»l.a 11-1,- J i ^•^ ^^-.™~-4~--V V<"^ 



1 



^J 



c 






Fios,. 26"8r to 263 Tofaf€>.77 h% ^6% Yo 860 



^^1 



I '^IK 



N 




A» 



i... 




§ 51A6 S ^6-7 

















i-Ai^L^^ 






I 



U^ vM 



» **►• •% 






"3 g->5" FLEX URE. SXFARiNG. 22; 

A\t.^)\|inf 1Ki5 "[orniula. to Exaivi|?lc 2 § 2.6 2 ^ vve firsl' K<^ve 

3 X 2 ^ [2 5 6 ~ I .Sb] C^ - 3-5) 6f--' 

vwKicW Cast |ror» »6 ci^>tvn4amlj/ aWe To %v/i?n sIamcI in sKe^^nr^c^, 
for a HOtl-OW RSCTAK<oUX-A^ 13FANA^ 5;^fv^»ai4Kte^i 

COT'ii^fs) bu'i "tbcu b^ dcnofe^ He sunt o| iJi€ wUrflts <?f Hi^ /u'iltvw 

256. SHMRJNfi STRESS (N THE WEB OF^NTBEAM. 

[i Is u^^tr^^t ^* CoH.5,'idie( -iWf , wiih I- bean^^ (a^ box be<MM«'j wtKi "Hu 

(lite (a.sl ■f«*m^bbisoM^'J«dl<> bcm^ 4<ik«H 0,-5 6)i«4eym of -Hte serte^ 
jV%iF) Wj^^d;r:-Fi-^<?- + F6i^^ (titc j^n+ it<m aj?j?rD)c.)wc 

.•tialiii" Fe a,*- eo\HioAV«<i wi+ii ^Fi a.iu:( 6F, . Sicf' fci, ■/i^ is w auiea 



I 



eciij^ {?^ fitk SAicb t« 54 ill tnof€ n«?trt>j e^uuj -fo X^to^o (»«e e^.^ 

io !?c<|W€H +c4{ie vveb «f 4/i* /6"^-ijici\ wroviaW-ir^n roKe^i beixmm 

sK^^xrl^i^ ^t<«6S a« low OS ^000 lbs. bi^r gq, ii* . ( fllitf f>t«^t«£ of 
ihe N*r. Sfeei ^Ifpn Co,);fk< web bein<| v«44Cai . 

iu^ €^K^i it) fusutl ^le load (q^c ^otU §i^*^) w« K^^ wt4>i t^--^ 

(Unih^ iMckaxid b^nM). Tke l^-inck /{*<}W bmm (yf fi< HJ-d^ 
k^% a vvi^ y men -tiVtck , so as -fc ^mJie Ut^a. %hioj( doM^ tk vul- 

iiT/. OESiaWING OP ftJVETIwaFO^ BUILT BEAMS. 
Tkc ki<^4r (xr€<3ei*^'a«\i o| ii4 I-teai^H a^U box ^ws, m^dc bw 
Tive-h^ "todisWitr Anii.iuWr (^ cdK^ivwictt^ 9K4^tVH^*^^f "Hue ma 

ttv^ft^wrt, a ^'v^^tHcacl $.1ie.m jmw' ot web, loitr \u<i^le4v«^i&**^iigjl 

ike dcAMbiUcdvou^-rO'Yv^^'^ a^luaU^iAtd b<Ai^% wliosc^a|<& lc4^ ^or 

IHOiitw-t 0-^ i\<t:(\icKj lioyv€v*r»Tk« |3«t'H<»ii c^ <»fo->^ 2«j4Uu 6*^ olrf^^ 
ttt nv<;i bole^ iH*^«.i Vwdi. be Uciui^. (Tkts wrtl be UluAWWiw 
01 \4uls'^€<j^u,«Ht jaa^xoraj^k). Tfe* *afe 1^ fwuti^i^ b<^m wmijjudkdi |nm 



I 



§M7 FLEXURE,SHEARim^ 7f 

art taoAeA io cut lD4ri<i*f «$ n sttitfte e«»%4M>«Mi rtj^ "»iWfti. JHl 
(i«dv>v "Hit th€«r CfitfV^ by ilte ti»<*^ e«nn»rt*H '^^ 3»4«|l€s i*U f k»- 

tiv^KkH'i pf +kU sl»«dir wAJj |k etvn^MkfiW |r«**^Wf!^IM*l4iit ^ 

wkitk He Web |0tM iiclfiwi^/iH c*6t. #t i^^ &#i4jl -^m^i ^«tt «^ 

b« o| "Hit. «aiH3C a^-mot^tit M» hofi?l4>u^ai unit «4 }«i\^?H m Ifce veVfi*- 

•fr^m S 26^ ^2*= !XL\ But iKe sK«armme vc^iia? sec- 
h«n «f ttte we)) ^ Wtn^ (^ri^&rm\y tiutviUaftd ^ ts lie S<«me B«v 

•w ftie vertttfo,! section of weV s:::: J^ iKc *^tcVl $Keav ^ Yined 

v/€lr> Wi(!i the An^Us) in o,n^ leeaKry «{ a. W«)t Vcav^^ mu^ts^fjir' 
W ^tLsfoLtn A shear e<jM^l t* X*r W«Y^t c'f w<?>\>^|5«r l^dtiz- 
*pe? %^.iutfe'^iva<iiw4att€is* twilic vWfft (m*mk\ lY6r),fa\<i l26T)^lfe 
^\4.^^k cem|?ve^9w< tefii^"^ lu-Ht«fti<<£ cf tU•fiv«•t-fuk,'ijieA|'- 
i4^ ^W^ acetUu erf +(»« tlele bl4m'ifc& (wea oj^ re/fereur^. 



J2IZ F LE^XURB^. $HE.A'Rim- ^^ 

dii^si&^M^i wiiiek $H<?u.Ij^ I?4 'taken iu\0 o^cuvd in c.o\i9\(ie^l)^ 
iki^vf 9\€^rW^ it+^e>v:)ik ,wK<«A tsittat <^«4tVf€| >W»« cemtec^v^ik 

^kt< Uv€>ri<jw«k 4^\!etMA»W wviKtk 4kM^H«^, vetiic^ all fliers in 
Wit -^iifl. e4 T fWn^ iv4^ «^ 4t>tie YWdedl u}^e?t ^^ifm Wer<jUi^[s<« 



^^ 3 ' 



tuck atvi^ bi^Hi). k^m A «*i^Ji^fi "H^t nviti^iw**^ ^astain -for ^ui* 
MOOO -r-lC m. ::^S,OQO ifes. ' E<!iefc rivet, having «tc«ti0«Al 

4iv«» <i«:irfimived'Hi*s)j«AWi^ o|'"Hte rivets 4tJ |#(Uw5; 

2^06^ iU, ^SA70 i|iv€t 0.80 fld-tlu mwWr «! rmi^ }w 
inck •^ kiwjiti #f fccant U. "tUi^ Hi^^f b< I 4- 0.80 :::::■ 3.3 iH<(i«5 

ff*w€y<r "-iU nvfH «kc*<wy ^idf b« s^e<i closer *H«in S J "hijjfs 



_§U^ FLEX URE. SHEARING. 8t 

ivi Tvwo rows (XMA oj»|JOAtk (^iu)?airs) iko. safe slieama t<'^i3'Vanw 
ot a bait (eack h\ stitnU ^Ucat) is QOOO Lbs ., vvhiU f^ sA-jt <^m 
j?maue V€KUWue« of Hi€ sldUs oi fli^'Hvo nvet Kei^s in 4fe^ on- 
<j(« it<jw« Cf lit ^(xy^t, [jUte belivcj niueJa tkUker) b j^^ 10(^^0 /b; 
H€ViC€ +^ former f^ur^ ((jOCO) dUi<i«^ tn+o JlO0t> tW.,a)vf$ 
O.iA 0»Mit number of b<Ur^ of tivd* )3er iiuk- o^ («uaik oi-lkc 
bo(X»H;u€., tite rivet* h^ o»i« row dliowU fe^ aj^aced S.o i'Mc)ffs 
oib<%Yt 5 ceai-ve "It) <*€KtY« ».Ue<xv (X 5>uJ)j?oftj ^it€ biiervoil +6 he Jm ^ 
cv«^vee<3( nv i>\v^fs€ Tractio io He cusia>t«« ^xoynMi^ nudWie ^^ 

Ij 1ti€ (ooui IS conceniraW In '+{i« m'tdlxiU of •ili^6J7aw,h»^Ac< 

(^<i fic^,JlsJ^)<XMd 4A* rlvcf«|>dc4itaiiiw^(3tdc<7rtAiu<^lij te^W^ 

4kcsanvi oi oU lo(XtU'H€d o|i^€ beAi)w 

3PEClMLPK0eL£M$ /N FLEXURE. 

/2^^5. DESiatliNa CR04S SECr^ON^ OF ^UliLT 

scivi'i. Take jor IWoiws^cxbuirt I-bewn^ ]fvc^.iUl»jOite vtiriifial 
gWni-^Uk , -foiwv cutolt it.TiJH-5 (eA.eli »| s€ctt©uai nr^a =. A ^ rcwoat- 
lu<jj a|W "ttie ikoU^ a,re jjuvtciieA, wiHi ex c|<aA/lhj (^ri^ [?<M^(xllel 

oji^ vvi<lHi -' t, a>K3( tkieknccl := t . Lef tit. v<lu>U <Uptk of <^lvr 
diftt :r li » ^}vii fKe diiixmei^ c^ a <*w€t W^ «^ t^. To ^et\j rcsUt 
the leusU^ <v^tdl (it^mbre^stvc liDfcci^ lk<iac<(jt In +fu!) section bMflll^ 

tna+tc) v<t iiiUit h<u<< -from §53^. ^,^ 

M,„=^^ 0) 

R' foY wroiA^kf UoH ^ laOOO tb^. bc^r ^(j.Ueli, e is :=: jk, 
wlu(fe I ,+lie nioYiieKt ol tHtrtia, of Htc C4)inboioii ^<ic+ie)a,b ob- 

cuiovd -^oU 6^ "Hve mcckrtoil. Jiidi«<Uiw!| witti^iese^sHoas a^iie 
cUM^lc^ avid -fWjes, VA/e con^u^er "Hve»vL (vojiCeuftai-e<3( dct +iifir 



^.^58\ npXUpF.aRmAL PROBLEMS. ^2 
cfwiui o| rtYavi'k(<vti: A^.|)|^fr)c»^v<^4fr)i oj- c<?Kt»c) ancf ifr«<d f/tciv^ 

JdFz^ (see §86^). Th< ^^^hh(uif\xe mc^nerd^ o^ lM^4la for 
V\t Tlvcf Kolfe iu"Hk wcfc ouct ^tvuiUri^( o^fJre^sc^. 

now b< wriH+€K .^ . 

Mi<fkicK is <xV(uUbU -^tJir com bull u<!) oa\^ o^t uu |<h onv it q^ntit^. 
T\u <^uaH+'iU^? eancetf x«d^ in I art jjo wicymtch** o.k<jI i4i4y 

i.KfXmjjU life besi +o cu^jusf iiii cliniiiuion^ of I'U^ secfion 4t» 

of nve^^ need ivot Vdur \j nutoAi Ivi cii^etvt coses, hoy tli«.. jiudt- 

Iv ie/^ iiuxu ^ or iiM)re4i<x.iv -|-iti<Ji "Htickf Tke ti^vjie Co. fe- 

HjKAfrtPLt: . ((Jnlh/iuekixudl pownA). Abuilf ttwi 

t| A ii^ y^v^h a^i u^i2c(, an^U ttoaa 3" A3"X V , mii«^ 
«.i Wfi> -^^ iu ^^^^^(Tie^s , OLvwdl j^Uie^ iiH(^l\ +kVek |^r |(ai^- 
«|e$> Kav^ y^iA* (t:r?)ixa^ "Htes^ ^n^€-|3(a|«ft hf f-ioiajji} 
U -22 ti»th«6 ~ UWi Keia(v+ df ai relet* 



§ 2S 8 FLbXUK&.3oitTBE7\MS. 81 

v-i>a>^. iv/t joy \l>is case ti» g ^ I, XA'^ieve "W ^ u^t, tota.] ^i^- 
1y»bufed loaA (melasma iKe weigW. <y( tlie girder 'JantJ Ir 5f)^rv. 
Hence tKe Icjt h^n^ metntev o-f e^^* C?^} ^educ^s t© 

_ ^6 \'^ /6 >< 12 000 

Tiiftt iSjttie tola} V»"»om€nt o[ \neYt»a of ftiC Seclvovi ^^<x*rt Ti<' ;:- 
|'^QC> "biaixoJ. mclies,. flrf vvmcU 1W web a^-icl oin^lt'-^ SMJ>j:.i>^' .:j, 
Kvic?wn <xmount^ Since % ^^ J :> ** ^ ' .*> "^ "^ r ? '^^ ~' ^ t** 

wKiIti \^t rerru3tm(^<?r tiiust be AArniskcd Ipy Hie f l^^n^es^ lV»us 

'^^ Sflksl^^ Ci^^<^sf\ y o"f <^^^ avajle i>^i^ 1$ -found iKas ; 
TKe -full secb'unal flireoL |oy llie s»ze ^iv€n =^ SX'J 'VS^X'^ 
-■ 2, 7^ 6^* iviches^fem vvViicK de^wctmjf "Hie two Yivet )iQUy 

Ths vcOue a^ O.?0 f$ ^€uncl Vy cwllin^ out \he sM:it 
c\ two cwycjle^ ^rom shfet jVc?vi ^ "thus: ( 'XZHT^'Z^Tck, 
av\4 ^xxUv^ciif)^ \t ovv a knife ec^e. (/^^^ ) *" ^IH— --- 
<jttp$ kft "b*! ftc rivet ooleS \y\ck>j We Unc^cdjV. ^ 

Vv^VHcjul Orecd/ error ^ m {inA'i*^^ (x\ H«vi<'e^$^W«!i4»T>a MA«h«v« 

I^{o.wek.X.Lx2o'^2Xi'|rn]':C UZ.3 

wlieue^ i) - >^.^ -^-/.^ -: 6 1 i)^c\xes. 

\U -n^ixhe^ ioia-i vvUtk of €Ajch of iht i'' ffa^u^e l^bUo TW5 

\y\\<\\\\ j:)e tVicre<xjie^ to 6-6'"'' $o a^ ^d e^^woU theuivild w»lil-k(?f- 



vur| {3^. fhe Uo^t dlUwctbk Ihtckue^i? ^{ web nv oYcle^ {o k^^^'^jjfe 
e*Wvhur| stress <sjs Itm ouS J^OOO tk. b^r^, iHcKj 

TUiS girder wUi n^^i^f vev'tioti si\<^en<yrs iie(?.r H'it^- ^:vui*,a^ 
a livj , B w^l I beaii li 0/ doicb U we* bs , <? r ttox --fo^w , {$ ee -^iCi , .2 6 ) do 

25q. SET OF ()/{0^ik(k LOADS. When alecomoHvc 

i:'ai5«ve<3 c^z-g^ a number of ^d.'<attei bns^^^d'(ic qird^t^ , eack oitc ot' 

'.N li I ek fe> be? We^fj certain dei <xciied ^t €/?i $uTes 6ot r^'-s b<5 vvAi nct tr 

te^i^iU^^ n^flk^ ntoiHent, M|^^ , a^td +ke i'not')c. sIko-t T^^^ , for 4^3 
Kiiiic^W l^o^Vtlon o\ ihe vwHe^U , 8u:t iiie-valices ef Iv'l^-^ and 
.j^y^ |or @^ui€- AtK«-r tK)$clion r>mvj be dir<idHr 'H'iau, ilio-se ja.st 

a^noi-^ Hie iK^ivilk 'Utavik.ro|(M„i)'s (o\\e Uy edek j:)e'5-ytb!(/ 
I .'»hVIvo v\. O'f 'H\.tyyiUii% m-\kc^^}C) 11 «t> enc4eKt (-rOTiv ft<|.l-3^', 
."^rowv 1ke 'Hal u*« ^l- ^k<i^'mo')iH\d dliacrravn , -fiod- v-^h^v 4ite jyi^riimji 

'\3Cr^\\-lt)V* 0^ h\t. tooAs Pj , P^ , t^.. OH H^ Spall ywiU iliftrti>u^ne^i- 
tiu. ii^M'a vilvv^^^l*^- H^ ^ "ti^ ifell^ I ^^"^ VojoabU c(ts1t5i.Hce -^ob^O 



3^^^ FLEXURE. ^P£Ci AL PROBlEm. 85 - 

ik'^ ^vfQd d(9^>u:^^a^etvireeh lh£ [ocxde (v»/he<W), Far anvj vdiu^s /;px, 

Iv, (i) wc have M^ a.<i OL |u.vm:.Hoii 0^ k ,(xi( itie oiier quuxn-Htea m 

(For tkh, OY awu otU'T \^alu€ etx, ol^Ms toIx^ i^ Hec^cd^Vf, herice 
D\v. one Ude of.. +<t€ "Wildlflliitol l+i^ 5]p<»*^ dus P^, H cru -f^e eH^r; U.os 

T'vv tkb fva^j i H .\^^\^ |^<xrH(ialm' case w«. uvaaj It^vdi -^lie ^e^ pe^iv^ 

rv%Yt-~R*I T t |t)i safe looJiiiu^. 

/lt> io ^Ht^'sltcAif J, jov a<^WeH |?o$ll-u.n^ ijffke vvN^*!^ Hms 

od^iixod e'-^bbort . SNkm- lie IW nvovc;s Wa^^d e>vH*€^ {^u.j?|;<?v^t H^^ 

wk<el volU eo\K|)Uk4\j cuet Os>\^ bevejdi i+. To jvvici riiA<XK., "H-wii^. 

ac^Vvow^ c& Hie suj:)j?of( tvhewHic l.o<xcU>vc^^ b sufteA^"3lvei>j so _^U^ 

A-^ fii^ VtVctjf . -^uonitul b dbt ti* e-oi}Le luwier five }i^%vi€Al" tooo^ -^Hwh 

•:■. V ^^■'He<?€.^S{?.'iy fo i^Ai wtik nt4>r<? iWv* cite j/v i-uuo wkeU ivi Hvdl- 



sas q hiEXURE..mo-^tHH loads. ^_ 

EXAMPLE, (iivew "Hu. ?D{(ow(fj^ wh4«( hf««s«r£-Sj 
A<- - - S ' >B<- --5'-"^<- - ■ ^/' .- -4) 

oil cae mil uuhifk H o-CK+iHtc^ics o^tf aAifxier e|~ ^ #» sf)an,4«;n 

/, /?e<^(urc<^ Hvi po'Stfieiv (;f Hu ^tsuli^ cf Aj B^ dHdl C ; 
2- ■'^ ■ M !j >< <; »> AyBfCf rmxiD: 

B bv: a'',vf.<x.?(, ? DiH«:- for vvKtri C. fteq<yi\^ tke v<ftii4«^ (5f- f^e'Sc 

HcH o-f iocuh. 

neSUtrS. Ci) 7.^' fj nqht of A , a.) 10' U vta/d of A. 
(3.) y^.^ ' to U^lit [- 8 . C^/'.} Moiy . M e -^ i^. 73 6O0' iKeUte, 
'fclHv (Xtl Mu wvbeeU ou 3 (\Ux. M^ iz. iUUDOOO tKo/x-(b, win? 
VMhe^k 8^C. avidD OH. (5.) Jy^^-IS,6 hm% di, nc^\ '^'u^.^^ai 

Iccwis, cHf vnodia ft| subpart, cr bcHi, ti*.^ ^utlu obj^in s^juaki a^a tk^ 
M„, -,1^1 (see §;239); 

vvii( bsL iuelt ik^.i fiie v^€<3uotimis are i'^v{i€p€v\(ie\<t 0^ -Hus jcnn cxiid 



I -.- * 



'^^^ 






X I 

i 



>''' 







F.-^. ae-v- §a6o d 






%260 FlEYsURE, SPECIAL PRO&ism^, S7 

M<xkiucj asectioii of m eitici \\9m\Y(^ Om ft€€ , x b<4MCj< l^ , S.(v«r^. 

T/i6^« iWues ol J*avKi IVl h.ol<^ Qood beUuCyt and C-, J 

nplil^ -rl. Tkls i€ +lte Tiw^v.M Ux jke b€Aiu, since fce'hv€<i« C 
aud B, IVl b jjrobarHon^l +o tke (il«+o.ue€ of ^le sectton fvoluB. 

.^^^„,=.^ w^=:Qf- CO 

1-^ Ike G-<^uaii:OH lor ^oi-{e {oAijliHA. 

\tih»i ifiS OK DC ; «.€., |jrduifica(Uj jil a dbve-t«il joivti eyh+c el au^j* 
^HH^f^ o\^ OC tiie foot Wow (n^ Ht« ^e^iin i)K fl<« ri(\k\~ o\ Sw.^k«<c45cH 
v^uiol clUc ciowuwavcis re/A+iv<>lv| 4o l-lic. left h^^vcl (jortioy^ ; iut vke 
uto.^ on C6. 

\k joivit e|^ abbl^*<^llo^l «a|:i.broack€5 a^u-jj^ort; Mih wou^ld v\ocfwal- 

V*'«<a ilu toad xvKjd fke SM.j5J3oft U ^ual U^ke rtAtfhon at fkfiu«iy 
awj->jp(;vl avui WiAAj 4-1 ta« d^cn red^fi ttlimlHuc^ N/alue, wheii ike eo^* 

H (i^:^5iWid ( wiU\^ , wt-iqki H<:^ W t-^' |3«*f tJ-vMl" o| (euc^-ili j b^(XJu» 



3260 FLEXURE ^SPBCiAL problems. M 

about m <ju6 

^>^',on^, (VI^R^x^Xyvx^ . . -_ . (p^) 

Hvlc(«itflx( ^Y x=.o (U. ectO) W --0 ^wltik -for o* ~ i^ (i.€. ccl C) 

5<2^f(ov\ heH/mii oiHol C, (i>t^ /or a value ^| x ^C^^ iv^^.fe)j$till 
between £) A*vi C , we bw-t (J M 4 ciy ^O ^ <3iuo( otfeini, ^ttb^frW:^!**^ 

(ji) wcK 0C4iwr CM OC OMi vuili be {{v^sr ikii^ Me (Dt<x<^v<t>M3 H 

OC wcixW. be M^ . 

For Wt<L 9)1 ort l^oyii^iv Be ^ whlcii fw.^ vw^vvteicl^ diU i^i^e^sa diou- 
(TfT-am'a of if^ owit ^w-f coKih'^cu*^ vvi+k i4©*^e fcr OC , tt ifiia^ eajuU^) 
be iUouvn ikxt- M c t^ "Hie ^ft^ctle^f lu^jHteHt of ak*^ secfUn ; Hmca (k 
fVj mci^.x^or 14^ ^ «f rtie wVio\e beam 4ii eifliey- Ivt^ ot Vi^ ^ 

knee c^ P frorvi %e nn^id'Je of IKe Slpavi^: 

J^inv*^ Since -from C^) and C^) 




%26o FLEXURE. Special P«o3S, 8*? 



!kc e<ju«Tion \oy soft louring is 

K eitiier P ^"^3 1- ) ^'*' ^ ^^ ^^^ unknown. <jiu?rhlity ^<3it.g>it^ 
tt->€ cv«l«v»*oh o"[ Q6j can not te «{>j»l»c^ an<J we •% use Ufii 
eijLuitton^i) in (^3 ^'^ ^^ divcrvy^mote Ijelw**^!! fiie Two >>esw)t$^ 
The <:^tJ<at«'>t. i\sZQr 16 J =r "R 5 it* F^^ 264 wKfirC 

26K TWO EGUALTE8MIN/AL LOADS. Two 5\1«^ 

MEfpacAL SUPPORTS, Rg. a6b\[Safv.dcase as m f;^. 

fr<.€ iat^ciu Om w\Vhx<li .- 

Px-i^-0 -MVl-P^c Oh 

wKik vv/k<^e .x>l, <wi<j(<i,-fl2 . -r 

^i/u:daov^ 0) ^^•■^^(^ C2^) 

0^ OC J ^P (^j 

On CD J =:-P-P^^e9C (5) 

U/-. and (6) yy^\jOih\ ddsa b^ akfalne^ fr«m (0 cuidi U) i)V| wrlHuc) 
X- dM -rdx, bi^^ ike Unywtx \iiethoci ts +o b^ |)r<^crvecl U 
-^uc r5a$«a elv.te -l^^ IcxHev re<{ulre3 iVl *h> b<3 e^cbvct^ei as a. Wi- 



§26/ FLCXliR£.5P£C / AL PRO0S. 90_ 

1-f +U beam i& avv, I~ b^m , i^ic 4<^J^f fkcA' J h x^ro a)U|~ 
<xtoK<:; 6C +t) . tuwit, "iiu "twe -fla^e&i bt^ He iower f(<XH<}« b«lH^ 

J2d2! (jNfFORM LOAD OVER pmT Of THE 3P/V^ 
TWO END SUPPORTS. Fic^.^U. Lef Hit hcKd-^^-'W, ty^ 

l^M^Hx. Ht^i^A vv^tjfet ol hic^m . FoY (K ^rte bodtj Cm cfca^^ k'n^^^ 

V¥?i.Ufi h(?(ct3 (joc?^ -for ^i^vj «€ciCm OH £)B, A^ hr ^ecHov^^ on 
BC iH« wot(2 ftiHtji^ie "U dee^-l w\+(i -Hte |y^ boixj m'C, of In^XjH^ 
x'<CB -from wKicK w<t Ikjiv« H-R^^x* - - ^ - - ~- (i) 
vi-^ihte/i shows -liie Htovnejif' Cittv^ -^r BC h b«e <xe1mlQk+ liueD'Cf 

av«. cVv^U {usfe<u( of (MJ'iucujftVKj wttli ilj (el tiu «fu<uuV ^ko w >sr^ 

Tk« 5(t<saur for <vw^ vdW. *{ x ch OB h .• 

On 06 ^ ^ > ^ jr=. R^_v^x (3) 

wviitU 01^ BC — - — X ^Rji:=^a>ii%i<xMf - - ^. ^-^ (4) 

ike j:)clut D luuih oeew-r <;k OB, ae wUl be seen, oW w\ii^\ 
hii t(i€ Mv), for tW wkok beoim) w« bv*t 1 = tu q. {^3} v«iieH<i« 



f^m. 5S7 t« ^V *fo {ace >. 9t ^§g63 ron% 












=3!K 









l^ 



V / ^ > (M l I ii'» '—';;; ^ — 



'"^ti 



n 








-2 



F.|,a70 ■^'" § 367 







W. Thl^ v<xW of X «44)^lK4^ Ui <2^,0) ^ives 

T^u incxvv eti€<J^ J^ \% juiosd cCt avwt i^ r: R,,wfelth 

263, UNIFOff NV LOAD CYER WHOLE t-FNaTH 
WITH TWO SY(Vt(V\ETR(C/^L SUPPORTS. Ft^. 56;. 

Willi i-W ^tfxflou g?cj3rc^6e<i m^4i€ ^'<^i^re, -rtie^Kowmcj n,- 

T^acfioits , ecuch -- jW^. TIi^ wi'One^i' Ci/trve i3 ivtcijc i^ of Ws 

if-ilve *u|ijj<7rts cjure |ax cndKok (XJ^^xt, m wKlck Caj6<^ (see. f^.') 
ike ^i^+tc oi^ne (r-l He be<stm tfeelf ieconus cxoicove u..|?W(!wrdl 
Ui-we^a ^te ^(nuis £ andl F tf '*co^+YttA-M jl^KWne'l /Ife^tdi^f 

X%,o^ ^fWc bchvH i^ ^>i4)'vvt€>iV oujcu<i cxa^^e't Ij^ (mix4>ydoim3, 
"^l^ee+lw:! ike dA6jcif(xm W€ iJ^c -HuJ^T li w^itl he dfW af H' Ik 

«' ^It ^^ 8^^^ 

VK<| a/& i 13 > i>r •< (t| /?^ . 

Ttw« ^k«ay eio5« ou +ke (eff <?| B-wl, wfili'e cfdse4«ii<? 



^K 



§26 S FLEXURE. ^PBciAi PRoes, 92 

26^. HYDROSTTVTIC PRESSURE AfiAINST A 
VERTICAL PLANK. Ftdm <Ji^^mch>^ h^<iw^iaah$ m^ 

X, bclo^ ^ fru.v|our« 5 a.K4 e<jtAA,U fde weUKf era /au$m ^^i 

wkerc V ::r vvetcjKt of o-CA^tic uMit (Ue. ik-e ii€^lJ13^i , see § 7) r^ 

Consider (?m *fve€ • 6e!sl<iU8 ^-It^ Q.lmH<i j^rcet cf^iii<2-€Y- 
po$>tA ^^Hcn Til, ftt^ -forces cmjUvui ar^ fW r«dcHoH K^^ tjLRc( 

a\vdt five, sum i>| "fi^ in^meni-a o| fd^e JK^svvYe^ ab^K^m 

h C^U<3il 4t) Mxai 0|- Ik^iT r«^4A.lHM^ (rr: tWelt fi^m, 3CH<^ Wi'C*! 

[Fvoiv (.0 wktn y ^ c , we K<»v<? for Wta "Wal ^^^^ br^eisjuTC «^ 

bom* <xi D we imwc ff^^ ^ "i" V^^ J 
for Om -nee ,w^ fui¥€ 

(wifvlek WcU <^at)<i ftoitv v-^O ioxr-lY Frcm S:^(kuriX'f«^ 



■ §^6^ PL£XUKF-SP&CtAUP^ 0B5. ^3 

d^ micjkf' (xhc kcive be«u ofa-ftUHAd h\| c(t|ferew"Ha+t;vuj(^J,si>ic^ 

^<{. ^ J aW ruiixte , and vv€ Kav^€ 



e ' ^^' ' e 



"9 'VT'V 



UKBMMPLE, I^tlt€ Hiickum of +ke foiaukU K,rqw.ma 
li- ? , if R' hiak^vi z^ 1000 its.jierscj.Hv. for iin^her (§55/), 

v^^^Husf 5ab«i-iWe R'-iODOj I- JZ Wc\t,es ,vz:. 0.036 jhz. 
\m ecLbie-iHck (kiOkiH^H of NATiJt.W l^i ikU euet^vH of uvii'b)} 

B yytli bd ^voficect +(t<tf '^\U'tt % for fl/l^,, ::=: 2 -r- ^5 ^$M.A 
i4Dt' -|^? ^ ^m ^^ ^'^'^ oecar tu 'fft^ $ec+loH ob|>oiti€^Hie ve- 
aAtXiovtf t^-f Hi.e wafi^r [jve^SKr* ; tte fi<|, 2^^« Tf>«e ske^tracrvf 
ie a.joa.<x\svl(x here] e^. (3). 

266. THE FOUR Tc^V'CRlVATiVtS OFIHECR- 
VlhlATE OF THE ELASTIC CURVE. Jf yfuYX^M 
C^'\'f<^ e^ucoMoK o-( Fke ela^Hc oi'i^t for^uy pornon.6f^ 
[cad/d. be^^j^jow w/lxick jboffijH tite too^W^w^ of (ovKilkof 

295), o( - (X cokHtImjious Wc.(?c) (as tv. fk^ l^t §), Wt^ 

'•(■ci.kt-O. A,etJi (XViiiJSr^ feelwo tjou^e^^fccfiv^ cro^s-s'^cUfiH^ 
(^ xioiucUii b^am^ omA (et fie block fcefwe^n ^f/tewtjW- 



El^^^U 



■X; 



^26€ PLEXURE^SPBClAL RROBS. 9±_^ 

-Hue ^lU^l^^cj reldiio'Hii 

d^c.., J^ $ rt^ Mi.4e.(^ scale) 1 ,.. (^ 
cfj^ tU fae<Jtm iWelf ; aYWihj , audi net arH ftckl iikt H^^ S- 

<suhi^ omA (i>eHrTM^hM. Tlu eA4J€ ]u^f ixeM<^ i%%l6^K 
Kovv<iV€/r, e||€r9 o^e^vj slmtl^ acu^e ^iKCt vv U+k^ skxiiie ^*a:- 

We/* be^m, Humbert vuj bdiC'kvw/3iv<<,witit 



§ i 66 FLE XURE. S P ECIA k V tOQ S . 7^ 

iN»3. Hies c^envaCtWe (diS'i' d-^C) \,% '^mailvt ^nree eLj aud (^ 
/'lave e^Ki\l>x^ ^li^'MQ^ ^3 ^.^ 

. \ (5lie<tf -r) E I -3T^ r: — V ^ "X ^ C^Hst. 
Bu-t wnhVci obct ^ka e^juAtlo-n -for x^^^^i , U€'f(?r Wve fJolnt 0^ 

%.\ 0,K-a etna M-0 .\Comt-0} Ai^c^m, 

\t be €'^vtal4c I , avc^ u 4t) be r :s£.ro.,uoi^e' ^'rod^ , ah^I iV 
y>^a^. u (.U. e| ^jr^^^est ie/fketUn) Ih Hit eidfitc eta^f^j wttk 

iw5 I u^ cWuiAslvj 4iie OM.^ il? IDC ^|nft.kev% . Tkll ^iuM ^^X safe" 



§266 ^t f^fAUR E^ SPECIAL Pf^^ ps. q£ 

^. J (a. alitor, 4 .€^|orc<} — ( - ) j:xn<.jvis 

5. w (f.^ H a.^ ^i)=(-- ){^t^^ ^--^ 

^"67. RESiHEN'Ce OF SEAM WrTH' tNO SiJPftfRTS. 
-^vTDvi^k aifi^fc^"■'k u|?(m M^ te^in. 6^ <l beaux iH^Jptni-iuicd 

GK :.^ .Si! - C^) 

Auc^ Ft r^ file ^oUy^HC ofiii^^^-i^fttiiki^bcam. Pram €<^iu3rk<^ 



^h U7 rLEXUljE^ special probs. 97^ 

bu-i fk^ \m^t of & «-!tfiuA<i v^^f b^ tswdi coiu|Wgc^ mik iluxi of 
Ike «vtcr^M of- liu^ Vt^ mt^t, -forWc bcduns e^ti^ scuue'^nd.- 

j^n'vkcviOLl "K,^ iiidt teK^Jtk^. (Tl»€*^ -same veLri^oiv^ tipU.cjDod;^^- 
' : M'Hu'tt-elxf 3 bev cvtd +Wc elos-Hc tiiml^ 

,r<kcd woi^ - ^ft wpw' fcft ht§J^5' joY static {oad^j(^Hui f^re^ii^Te at 

-tvA.ck^ts'\ ^\j Sir Jokw Avcdler&on, UvwioK, iSSif ^\^u: (_|oJ?4^ 

tariik and dt\>V^ will $uLJ>)>ort, bi*.i ika+ It wH oe<xr ddif^bfelfe 

'sjv^iqk'Vs atv. us«dl , tit^ Uh^t b«x>H vytU net brecxk i^^j "Hte wei^fit 
v'Uvw^ tAjjcHt-t uile«7$ iS" |tilU tkrmti^k Ww€ "Htc ciUVaiu:^ recjiar- 

56i\a)|VmiN£D FLEXURE AND TORS/ON. CRAHK 
HAFTS, Ho.Syi. Ui AB be +ii« txa.uk,(x^^d H/\ fe>' 

A-^ dtrpj^iid |rom tU. ix#i-5 "OOj ot ^H^. -^Uff u|)t'H P^ixndh 
-: dti'kt.H^is 0? a, ais>vwj -Hie a?ds 00, ^ Ut'Hi iVte cro^? s^jciltm/ 
Wlu-\ t?i \->\9 ^^\\<x.^i, cli;$e "bike bea.^inc^. LeV NM' be ivciin- 



B^s, 57 X V. ^ 7 7 To ^ace }>. T8 % § 2 6 % to An 



F,3.2V2 



,%-^ 



>,r.a- 








^cd 



-I * 



-l, 






nisi 



a 



T 



R^. A7^«. §5-?l 



FVcj.a7i- %^'rx 




F."5 a76a. 



F»^. 277' '§^7^ 



v^/«i ni^Y <3ijJsume MicttHie. sfif€»^€« it h^ ^ui-'hx d\\ iks eM^mriH of 

Hi€ $keciriix«{ ski^s it^aevd "biii* di<^cl€5 wkui^ kdui« cts aeotn- 
\kev\. e-fevdre , audi |>«^^ 44i,tiDtt^k "Hw, f'^p^U^ lF*S /or e(«m- 

acHevi 0^ "P. 

'^■^ ixvJii ©I owtA iK rkfi *\u<xil J3(VYd(teiobl|Mttai eiemetit va of i^ic 

aboui NW' fm ttu frcf bod,j (dit&re<^ardiiHi^ +!»-€ moHou) wc ha^'o as 

M.pi;u.f: = ^ ------ .. (a) 

\Hc\m. o| ik«, sHtCtfs has (X'^^uMHtui obfiW^ NNj N^)t+ kkoK^iuo- 

:^=Pa5i.e..|,,=:^ - (M 

SiOKal etauRttc forces , ou, omvij ouiar mtfst clF^o^t (rfjii^ ; aw(i II, 
V\ie jpolfluY u^onwiU- of luertitfw <>f Hi« urcle about ik eftilte 0. 

Hfexi eoH^\ier fr€^, iKftc|. 57:?, asiwaiil J3(jurc)L(te{fib;^€di KksK-fm** 
HivL keiu al m(of fif 270- ^^ 3ff«%se« |fe« ^AO(^J acK*i<:| 
(vvv -tke -ft)Wf fac« r+o ii-c )3<Lf)er ix Ut^, 3^5 are tkere re^irv- 
^cvdecl , H*^ cLimaw3.U^v5 (lu-fiuliesh'Hftii beiKtj n |l \t> Hti^h 
it lo 00, , (kiU d r U\^e |?ap^r Ufii^jyi. Bv( oiWivw^ 
Hi^ raHo o| 1) 4t> n «vt 'wu»| vtidke 1ke avu|U wk^ti- ^tjiidiKM' 
BU Kow [m>J8aaei it) c<>>c^\,dlef -{ree -tW ivujivujvdAr )jntj)*c Q.HT, 
H ftvvi tW^ iVL4ewi\H| ©f vuJ^niAi sHe«% 5,^ t>^ i^^^ of (xxe<x, 
f:\KV^t dU^owoS jpl(XHe (iHj(cf UKqtk = § lArVicti h a b^vu*wliH(3| 
fa^ of -Hiat 1:tlav^(]«.lcix ^\t\-}x, $ea jicj. JZ73. B^f ^A/niiH<^ 51 



^368 rLEXO^E. Ci^A^K Shaf t. 7?_ 

2^ ccm|Dcm^. m 4iViccru>n <?f novmal To GH3~ ., v^^e ska)) f>a*«e^ 
qc el = |>nclsw 6 +]>-W s«n 9 4- ]o^nc^ cos Q 3 a^.:^ 

O^zz y ^ Sm04- >yr|_S.t,e +-p-.Cc5 6l> CO 

"but n : C =■ ^in 9 a*wi Tj; C =: COS 8 •*.. 

^ hi5 t-n<Ky l>c WYirten(^Sce e^$ . S'5 <^^AA 60^ O.W. J, 
> r%AOri/Jtviehry3 

<?=^ 2 I'O^ ""^^ 26)4-'p^^ut 20 ^ (3) 

As il^e filtWonai I^Une GH t* taken*m cViffe^cnt j&cstr^aKs 
Ci«^.,a*, 6 VQywss)^ "^14^ tervsde stress Q (^ Its, ]p€r Sf, m. 
frA tosfa^i^) cAso vavj€S^bcm5 a ^uticlich of 6 ^ avid Vts 
iiaOx, v«lt4e n^«Ay be ^ !>« \o *|it-ui 6 (cr o ana^i ^ we 

'"' il=0; i.e. >sr^5 6-t-2-p cos56= o....(<^3 
Coil flus «aiu^ cf a,a'. Smc idu^e' ts nt({cdiH^,2B' Iie3 ci- 

rSv€ e^italioM 53 (X^ Jdq TVl^dHometn^ , O.W.I J The t^f^ 
;)i(^ri5 rc^e? b five ^eeW ({t,«ju£ r cuit ^ f k^ lotw^^r it> tnc iow^rRu 

^^^2fc^2e-4^p^stu!l9 - ^^ C7) 



i 



§.u8 FLEXURE-. QRAm sHArr. ^oo 

O^L0uifavst)>T^ jtW <^ max.^ fken y^i 0' for S iv^ (3 J <,uX^- 
stiUttmjr frotyi {^6 J) (^«*^^ey si^^nS^. "W'e \\\^S find 

I, ma,. « -^^J^V^^ il) 

ifS ccTi^|j?c%^*m-» fnt^&cLfil af tcft^Wot^i ^ ?%^.tf«ji ^.^11 mH© le 4ri?v»'i- 




6uhlc Indies .\ r -r-tStJ tHches 

f/erttWiVk \y\&.%,<^^zz 7000 ^j P,A, €iKd I as before; ^Arm 

Tl^ir. Utt^^T i^U& ff r,l4/ Iv^d^Sj sttotcl4 be adej 



%26S FLEXURE. CRANKSHAFT /of 



(vwn«A P -^- UCOb ibs- anil a ~ 6 hi.) -tkat <^ >na?t. (and i|5 

Ic^ee P (v€rHc<ai eoa -pressure) i^ ^jp'^Weai Hi ^ver coiiinvcNfe 
T'lioi- ?s,4ke rtcjict Ixr^ O0K^hfCiu^ ^f-tkc+i^o wlieeb <^Hd 

skWX be elHtev f^ Ij , at C ^5 ey P^ I3 ^ at a Tke [;^rKdic CD ts 
iiuvi^r -^btBloH , o^ amanu'rt+ oj 4^v^Vtni ^J^ (k^^ Q^h^ . Heu^iciw 

FLEXUf?E,C^NTlNUfcD. 
CONTINUOUS GIRDERS. 



l^ iMli tbiSj^lisil fe*9lk A^ wKieKe«^« we can •]«) io>u)erja? 
Ker^io lort , ic^iiiint ike t«a(rHons at 44t« s4A^<nrb -froAi sUn|pl« 

tiu (dHt/r vuetAsj i4i^ be ^and tn i^ ^k«^ w«-e ook^ W^4 m~ 

«.oi4.'^ t^^.m^x o^^ two ;)KJjf^iw1-^, th« reac^ehs ^Hm iMdepeude)^ 
' A*, o'.u ILLUSTRATION^ Ij lie sttatcjHt b€«L}ri(jf ft(). i/^^ i.'i /?iic- 

sir^^^'iiuj tktf wKdIe beam jre^^wa lw<t iVa^ unkhowH c^mkH^'^^ 
avs4 oul\j 4w«> ^*u«iidK<i, vlx: 2l (vert . ei>wj»H^) ;=:0 a^^cl 51 (jw4«h5. 
«3ioi4s0m€ |5<?int)^0. rt U£>w B b« ^«xduiiii\j [owcmi, ii re- 
ceives i^^ ovkA leip? J3iif€S«t4y€j kkIU tV]>4HSt.HN yeacii€S (XjJosiiiftn 
^H eve V»t.€ beam W^Im touAfieij i4;a**4ww 0*$ vteujVbn bjareiD 
■Uv^*! OMd C SiAb|>«»fT Ike b€»*«.^«s» \lo were uof "Htev^. At:? h 
K%vu Uvu B Viwt^r "alrtk to alfcuui^u^ p<>^Hi>iv,c{«|jiK(is cj*. tii^ 
isii^n£s£ flurui Uai •t Hic k>€».ui* /Win , i{ 8 k «u^ (Siisy^ 
rke ie^l cf £) €UMi C It receives cjTf^Ver OLi^d c^reatesf Jitree^twrej 

Uovt^ wouJct te diW^^ |-n>m ^\\a^ "Hie^ w^uJd be i^ He h^\\\ 

ov Hi4?. supbM B,lK^V<24i4 <5| bei»vQ <jtd a^rtcd' 6 itcio tyv6 
^ue^jiv:w.cievct Iftaam^ j. ^<i.U. c^verht^ lb Z)wh sj^oh cu^^dt kiWhU<) 



§271 - FLEXURE. COHTiHUOU^ &iRDE/?S> /QS 
All fke oases (vc^ eo^^4flt«^«< wiii be coiHJM/alive)*^ siitij?^ 

dtciAUv loike beam avid vw \k^ %An*e |^t<ui€. AU^u.j>j56t1s ai"Hift 

^72. TWO EfiUAL SPANS. TWO CONCENTRATED 
LOADSTONE IN THE MIDDLE OF EACH 3PAN, PRIS> 
hlATlC BEAM. Fi^, 2.7^^ Ui o^k Mf-ef?avi - ^i . Nc^ka 

i-<jnu)a.Ht h^ke eia^Vm <wvrve dd U korla^cuW* ctad tiuet+k 
^lA^^t^of b arc i^ a, Uv^i ik^ ic^^e^ovi of C ^OuV4d B) btlow 0*s 
bwoitKf I's^erc. The %i^^ii^i2^ do^'Hc C44,rv€« OD aKdBC >W8^<? 

Fov fite E&l/ATION OF OD,VMAk« (ts^c+iou n aw^(wher« 
beVwv-efivv^ (xM D , coKsiiei UvJi i-iC a. free hoihj, Fi(\^ !l]6,\mii 
dvlcjUi aiu5i aices a^J iWe ludtc^tei. Fro hi ^(vvioih$. about vcu~ 

T<xkiw| +ii^« >c-auU-ci€VWa"kve o[ (3) w<i have 

a,-_P(i^.i^)-P„[i|i-^] (3, 

H^s€ aija.\K He* cojt^Wut \^ zero ^UeeotO xand ^ txfli^O, 
(3) i-^iiw ^uaHoH o|- OD ,(Waiiew9 \u>vaivi« c^>:<0 or>|- 
11 coKtalu^ "Hie wuKviCvrfA ^fce "P. . 

Fov 4k< efiJUAT/ON OF DC, !e^ +h<l variable $ftciltH n 
W Hv<!K{e Av*^vv.iv^f^e IjeiweevtD anclC cUvd^A/^ ka<r€ (^Fk^. S/6a; 
. v^ M.OW tav^^^c b<>Viwe€n -4- and I J 



L 



£l^--na-x) - . - - - iu) 

ftKak +kfc T<.«u.lis(f<r< tk«iv«« curve* H<x«e<J-co>i*ni6wi-fi.v<^6»a 

.. H^=|PlVPjl^-^-^j^i^PP (6) 

tiouT^. To cietermliK T^ we ewijilo^ +(ic |aci "Ht^xt 0'$im 

^ivA;;lrl(^\,s Ik (,6) we luxv/e 

Fvom iv/w iitefYM Pg also ^--^F, wktl^ T^ fMu^i ^tt ^-^ 
^(Moe 'P^'^^l'^f^c:^^ P,(vvKol« becuK fee) {jjolvJ[ He ^u))~ 
borb W'^'Ta >u?t ox a lev^l^ fcvtt t| (-fuif l^^.-^fmu-fij lite nUaUf^ 5uj?« 
ptn[1' C wvere a *^vuilt o(tsfa.ue€ =1 h^ b^low lli« /ev«l liuc ]ohuH<^ 
ike o'Ht<m , w^ skoiA^U jp\ii xc:( ^h4 ^--h^ iu c^X^I^ohM 

tW Wi(jft-Mi(v{ (Uv^ -tetvn u^iiie f>n^ matte*' beai>i avid u.pvyi ih 

^0 ^ 'c ^ M ^ ^"^ tv.<j(«? )KfMievi+ (>f "Hit VHaW)ic4 A-VMi -^>vt c|- 

.iklck wu-idi. +krn =•- H- P - (^ E r Ow -r l^J, is fauiKot io %^ 



.JK,^^^'- 









4-\ -. K'/^~;---n- 



<.. %.~ 








%3fto ;;-^^--' 



Tr= wl 




lllUlu.lH;,.,:t!?'^ ir -n 

iTTTlEniimii] 






wx 








^27Ji _ PL£XURE.coNTiN(;ou^ ampEKs. tos 

Tjl£ »tvoiiuiA <it(X4^VA^i^ 0^ tUU c<v3€ C(U\ KO*»A< be isa^vl^ 
c^>K3imeW' rtfij.577, Fdv ama( |r«« bcsU^ nC^ n /i/^tij(>< 

t.e. vane* dlrecfiy d;%;r^ tutifl x^ jsxi4s^B D wht*i^ |^au^ 

"^" ^«^Pl ~ ~ C7} 

The ^IwAr at C cui<>t cu^jwUr^ 6K CD -^-^V fV^hik ouW 

The moiucHl: avi<i tlic^vr dld^tonw ox^ ed.-iUs c<rHf^fma+«^^ 

;^73. TWO equAl spans, (;iv( Firmly distrib^ 

UTPD LO/AD OVER VA/Hei.e f.EIVaTH. Pff(SIV!flTi^ 
BEAIVI. Fiq.i/S, Su.pf>0(h B.OjCouaUM^Tatd 
toad ^ jjW'^-^wl awd 1naui( iu6lu<(^ fbi-^jf fH€ beam; wis 

Let 0)\ =rK ; tk^v* w'l+K h C -free , 51 ludms. ct^owt n:=>0 (fi^^ 



%272 FLEXURL. cor^rmuous, &iaDERs./0 6 

[CoM$t-0 for a,t hoik % avui i| arc :roj £(7ua+tC7i5 {^z)/^, 
and C3) ad^utl o^- Aiw value e^% 4ro>H "b c^ Le. fi^li 
cjood -fcT^ ou\w4 bonii of- Hit (Uas^Hc oawc OC^ Uml. loadht^^ m 

aui C are cvi ilv€ aMs of X) (jv^^^^Md- ack- O), WHk fiw^ 
v<xiu«^ cf- X aiui u lu fto. {^) we have 

Th€ fAOMENT yVND SHEAR PlAaf?/^WS eauiiow 

S^ f<>^m«oC t^tuce ail +(t4 ^rfKKal ^c^-ts ani /<noiMi» In 

m^fw-^-^ -oi 

\/Mh x-L B-vj maf?€£.ffoH \f h^e«M ituit for K--:^D, W-O; 
bft^fc^,Mi wtfkl<it\,+(}iA/ard O^-fke uj-j^^r fiires cjirg tu +e4-.^kH tW 

M^ -1 ~ 4* ^ i"^ == i''^ • A^ fo ik€ areJik^\ hvo>u€h+ It) be 
fi5uv.d cru £?fi ^ pat ci^ ~ (i)(J -0 aKc( sotvc ^-v x. Tlus 






€ 



But 1kU^m€.r(ca(^ [es-s +(tavt M^, (p-^Wl) 
(lesAce iti€ <^iujctiou |ov safe (ca^tu<^ b 

■^-ywi ^ a; 

il^^ saut€ as i| +Jt<i bcAivi were fnxA 'ttirai^i^ (it {?, ^outk Mf, 
e4-(,:2.)j H^itci ii\Ak'tuc|ii.€ oilier co)\Kituou« cft/eif'Hi^ )Hi<i- 

A^ -Uyf fiic 5jii«d«jX, vv€ o\}^^6xy^ !f-f^au«^ sec+tou fe^^ 
(yevHcitl |4nfciJ5}=:0 ^ m free bodtij nC,ai4^ ^fitu^ (iay€ 



iM 



uiK h/L; de€ abfrv«) olmL for k-I if r:--|^W wludt 

\=fw-' c^j 

Tli<. -nunHeKt (iM>i\t^ U a ^abota {(Xi^bara'fe 6h^ for eou:!^? 
^pCLV».),+lt^ sk^ijr curve astramcf Ituc , luduiedi Htj rlt^ htrl- 

PROBLEW. How wouU iUe. T«a<iievi^ \\k \i(\. iT^ ^^ 
<tkau^€<i r^ fli^-s^^Jjfx^rt wer*. (ow«rcdi o.^>^i<t{t) disWee 
Kq beiowv ike (cve^ of fli€ oiitcr k«i> ? 

LY AT BOTH EA/DS (AT SAME LEVEL). SfNfiLE 

LOAD AT Middle. Fi^.j^^o {a$ u^uaI titebpu^Hb 

(Mvie^d^ci "ft? b^ hii)uo<|ekfi^nLS ^o ifedtt" E b 1-Wesame d^oll 

3'-b^e5e(i 4o bg of sucK awaiu-re ote fo cAute iu> ftonxoHiul 
i^KsWaiuH ', i\«.^ -Hue beaiu. ci/>e5 -wotad- <^% (s. (iXrfA. or eUiH, 
i\\. auvj VMAuiRet , (Xi^.<i kmce, ike ^mn o^ "Hvc Kon3^0H4a( Ctxw 
^jftp>%*^^ ef^ke ^"ke«is€!^ l> auvj ^eefiOH H ^e'ro,ai> Kail 



§^2/4^ f- LEXUR£. CONTINUES d/RDERS. 10^ 
i^ftctiiwq CAiSe^ o {- -^le^ure . Ju otte^ werd^ lie nadtAl oixk 
^tll e^v\.itj(iKS Hie c«%vVr«. of <^f(WiV») #f Ikes eeK 011 cu^^ He inu- 
stoifs audi et^v|)tiestloti$ a?ne.^iMv<fct!?^^t" 'fo a ccj4«^I« {fUe. s+ness- 
(^i/iA^U) w!u)S<^ inorH«*d" k +k«*^Ynonw«fvi: 0^ -lU^ycrz^, 

ces itwA iius fwxHAH ,i)f UvwjHi ^ 1 , 04>MsXderedi free , ^ forces 

iocuij ; W^ icjawax-ci skeats J^ ax\d J^ ^d^e <>:^eac*K secitovt); and 
4 wo '^sfr^-ft - cotc^l^'', (^He In each, ti/^H-ti\^ ^ ww(u>^« tHorwenis aw 
^p a«^4L M^ . Pn?in s^jmindtSj we kuo^^ ilu& J^-T^ , ait<j[ tk4 
l\^^-!M^ • Froni XT -0 for 4(ce ff«e bo<ixj |u^1 vnawKtmci^ (b^A 
^t ^ivtnfm m Hi€ -ft(|uT<), a>Mi |-irfr>u ^ifyrimm^ , we Iiav^ J^ ^J P 

avwi Jc ~ i"^ j ^^ "^ ci4i3^f>ume M^ aiidl (A^ ,fke fcY^n /:-|ik 
ebsHc C4*-<ve3 OB ^xm^ BC i-vuas^ bn hJkew Wh aee^H+^cxs ^({.<i»s: 

tu.>v. of ttii? ittOmaiis o| Hie H>t*i<nis d^^d ccni|jre-f$u?H» ciig, 
cuqis of (? j {<rf 14tc$e icw^l=mis and c«^)>r^55tOH^ ore e<}Utvaf6M+ 

1-JXk<^^«. akcw^ a-H*^ 0^% wVlodr€V«r n fo "Hvft |?U*MS of "file C.OjA.J)i€ 

Tl^v f^m^Wt b Hot (xM«d a^ iil^ x^ro. New |<ov!i ^)nm€^ 
w« . ' w iW Ike itMM?«.vtV^(W lo HM».eu.Twe DB a+ B K hcn^:- 



i2) ijl\e us 

H^ citaw( iUe -vnomcv^* diagram an<i -fir^i M,„ . For co^vfinmicf • 
-meAStirc x -f^om (^ . Fo^ t^ -pre<^ ^<5^^ H^ , W€ have jjet e<?./.^3] 

\\&.u M = M^~ y PI ; b-Y ^f HC'r. M^ ii? scale [^o ^mnx^ t^ch- 

|3ey.wis WClit<U\-^S^ "Hit WKfrf JM^K-O^ M &, fof ^--J^Mf^-^^^ 

hexvee ky fiff B'D - |?l oiiilve e{)f?oslk sidle of +^c aic'ts o'C'^ 
frc^iv HCS Mid join DH. DK , ^.^-mmehtCAl w\Hi "DH ateo^t B'D, 

aV'Hw €>^<^^ a^*.^ ihi^ load ; tV n\«^^ afee b^ ^YOY«d +o be jcxAsc 

Tk«- fV)\VL"V3 o| IxUe^RffVL c^ -f^i* elastic <HtY\re .air* miioeWwi- 
diVca of ttve half -sjixuve , v^^diU -five incix > s f v<a.\ iti 

J275". PR(5M/HtC BEAM P(X£D FfORi20NTALtY AT 
BOTH ENDS I^TSAME LEVEi.]. UNiFORMa DISTRiS- 
UTBD LOAD OVeRTKEWHOUE UEJSfilTH-F^.£fe 
A^iK H^e precedliu^!) ^rt>ble\'n , \a<« know 4to>n «v^vnw€iT>| iWi 



§ii7S FLEX(;RE. CONTINUOUS aiRDERS. /tff 

cvtial ,we lUAy for X~ I ^ dt^ -r(iK rrC , OMd oktAiU 

aiC, 

^ iWe -f<f«« bdUj nO (^ levk^HvK, 4Wiis ^itiban«j 

i.e. M = H:'isri+-^^i:Wx - - - c^) 

AW ^wdi$ti ©1^ ifce second (iww^i^alicouHn^j accnk . 4f 
caJi 4 M.lwL5? >v\Aj(, (ntu>i<iM^ 4(rf M^oa n»<x»/ be ^ka^nn bf wriHn.^^ ike 

SiWc (wttk iiu^ form oj- ((wutous)) if ik€ beamw«rfiud~l)culf 
^v^ bui- itrnjiu resUd CTK.i^^ ei*i SKJ?t?©rb ike 8<?wlHwi ^sofa 

Cfcs ccnvjaored ^liU ike oili«r;tV^. wi r^^d^ %(3C}s\»Xtirt^^ m 
iW tm.W>r eiem^vfe . A« r«uj<*rti* j^Wrn^ ^ss^ i>.iW vr^b if 

As h ^iilfHei^ iWer -^-lie lAfji^^'nu io<iA ^ik^ )nAA/f* d^iee- 



I eat 4tK\^ IW ^<n- ^w^^n W su^jiK?»^ %X^Aj (>CH(!t4r UMi-ft^vm 

tke kovliUHvhfcl (W-s -Irom wiW^k -Hve {7rdU>t^^ ft|. Hie ^rnter cyf« 
It iv. "jw^W avHdu^ OS Wve e<^uai. cur ecu? be^nrc^t iVcaMl44i.^ o^.^e^ 

tw cVU^r wo t<is , live e|^^ af-fttih^ +k€,e4«d's tionxe>Hl(Xll^ ]i.U 
§iufV ik^ Yvu)Hi«Kf b(Vfcv)&ei^ u|»Ar<Mndt a dli's ftK^^^e ~ M^{^t? $'«a.l€X 

J27^ * REfeWKK^. Tlie ~^€q«i\^ w\| slmj^l^ causes of-tou^Mu- 

fip>^lw« f;yf SflL|e loaii\uj ot^cL f^rrciefCtciiOHS . Wlow. H^ere cm 
\yi.crt iHcu^ 'HiTiie 5*^rH^v^tlk tjpa^% of ufif^t^X kyLi{\k^awi 

iVk 1 257* B^ ^^^ "Ki^-o^^itew ^cjVvrtn* Hie 5(>axv^^ tke {^adhu^ifii^^^:^ 
Htc Y<5ift-•^!t* irwHalll Heiejhi^ af tiie ^uj?f?0t'b , vv€<xr€ e^tofele^ h 

to du4«rn4fei^ tii^- vmmMftcb ^ait ike ^M.bjs'crls {|>. 64/ Hankl**'-? 
/^pj?U<i*s- (l^Eeiiawic^^ Front tit ^tervwowsut^ fk^s/i 6iMff c(oi& "i^ e«5^ 
si{^.« of ^ocU su^^beft" Otr€ |o«.Hi , tk«j\ i!{< r«AfcK{)n^, <iJt<ifr<?trv 
Htfefit^ CLVii +k6 i^iUOK lod<3C3 Mill i-rv<mi«iAi'«at' a\v\| sec^te^v cak^^^ 



F.55, I^H )-o?8<fTo5ai.« f. Wl %^ 278 r« 3^3 




T 



THE BANfiER^US SECTlGH iH 

J?77» REMARKS . B^ ^ Asky^sn^'t nedfxQn* * h w^eant -i^af s-fif^ 
4U'i\ (Ik a cfiv€n b^om. ytvHks' <nMtn ((Wbdhuj wrUi (jtven mijrfe (}fsi^ 
t)CTl)vtk^i^ ifte >tc»rmjl ^tTe:5S ivike at*^ef |i3jre^ df" cG^tOiiee ^ 
'(^rouuW ncuiral (Xus.J,s <meder^\^ lxH*« (/uil&.Y |iljYfi cf ctK^ ^Hj- 

JiaUeei. U iHc irui^tr litr* ol iiils s<?c4i6n , f| f(i« (cod U <:^iJiiiusiw 
W^<lw. ^t'e^iusiiMft ^ ^ *'i L^^^^] ^^^"^ solved ^ |?^qlv»1uf 

fjn&rvuatic beam, \W6 ^jcjiir^e^ "Aie |V\ ^^^ I^ ^ytd ^H*^ €* o|(Wtv| 

CATED WED&E. TWO ElTiD SUPF(?RTS. SIH^tE 
LOAD (N MIDDLE. TV f<^rr»v is skvy.>^ tu R^. JZ^;!^. 
Ne>«f^ vtfeu|W &f h'^^)fL\ -^ ^ivfiuvStLte ?^ from one &upf>«ti,D. 

T& c^'pns^s 4kc C' ^ j;\r , clU 4!i^ X^^-jL by^(§5>^7J o^^ auHy 
tfiVfkc 4Tu,7vcA"t«d[ ^^f^£ k fee' hvo (c\i<^e<jl "h) ikeiv ivw^ecVlfiH 



^boo^^-^l ^h >c ;ij. wVj+ke dicivuj«^oi^s seeHonwtH fa« d^C^ 
-m^ iKlScUe ^ fk^ boa^ , as If 1^ beA*a were |>rt9»t«irt<j;- 



)Ni\ix-kl<C 



Z 






W^^^n^^is) 



6 ^ 



fiq.Z^S^ For "H^e +ruTi(MiW bijiivvw^ hcik ^idftk "=: u^aHi 
Kfcujfcf ^v are variAtU ^a^i l^ b ondl h arc ike (jliMi^^t^ifeHS 

t?x A , vve ^kdU ka^ from timiUwr irTiaVi<:^le^ ^ ^--^ t^'^^) 



or ia^pM_=.iPc ifitb>ic CIO) 



^2]g FLEX{;RE.NON-PRISIVl/n-)C BEAMS. 1(4^ 

•- i^c.3p-y#..fe!52!zL3±i2S£>^ (8) 

(W vnhuk V and V arc 4^ dLtm^sicHi^s <xt midt- ^fwuyi} 

For ^* 5FmiJH4ii«a:£D a>N£ wb«e e - Wie vAJriafek *«- 
oUus T , a*wi J ^=-4" fff^ ) wc also hA»e 

^=g-#-^ 00 

^mA h-ii¥^t p U 0L>MOgr.-f<?r ^^-^c^<m<i iftfi e^ix^£H<^R -for 

(^h«Ye r^ -radium o^ y^iid-sjsaK aajtiwi)] 

5:^i!r-:.^Po,for^l>i-c 03) 

2?0. REMARKS . A h^.^^^ toXd +o K ©f ^u\tC fi»mx 
sWn^'^wk'ea IH form , ?h Mi.o(k ef $iA,f>j?ox+j and i^ Als- 

0^ esovumv^ W Sdcwredj, ti:c«i jM oil -Hie etvVer -|ihif$s yyi^y k 

be — R. tit ail o| -Hw-iiw. 104- ^wn« > m all cases e-j^ jUxtjuv^ fke 



nvoi^tevd 1-5 i{^e ^avwe -for alt sect i cms of eD[ec|.^-?) o^-tii<i1 SJ au4 

III -Mt^ fi3Uowluc| ^jrobl^evH^ ik^^ei^[^t e\'-^\e-h^\M,\k<i{ U^%^•' 
Ucieci. Tlt<. cjevv^al \K€Hi<>(l bvifs«.erf will N Vo -{^x^oui ci^^w-a- 
3icn\ fen tW OiA.kAr-|^br«,-itfrt9'» jg ^ of ^ daf ^vlk ^eJ^iUn of H*. 

5^h PARABOLIC WORKmdeE/\M. UrVSVMlVJETRII*- 



AL. F^.^?6. CBO.Hai/vorkiua 



beam or lever 3 B beivu^iiie 



iuIcviM^ txac4iDK l^ f^ '^^'*'f<j • ^^^ "^^^ -fotc^t? are "H k-Ute 
b^^dAVv . Tk<? b^m U ii& \u>.y< Mae s&wve wldtk l^ (xf o>ii ^otute, 

Re<j^ired FIRST, llii jsroW Kelc^kt li^ ai B ^jor safehj. 

"^^"''•^ M^P/ •.. 4.iS4 ^^^ CO 

Fcf Ike ^fe« bodvj n0^we/tav« (21 rl44»m*4j^^4>) 

-|l :r,^^ ,wlikkm<xv| bewriM^H^^wf r^iy^iljc^-C^J 

;>.-. a.-e -It) make. -Hi-e rekt^A be"bW(??'i\ tt\c abscissa. x cvu<H^f 



I3i/ Flexur e. NON-PHisMA-nft beams. h6 

Tke joA-vaboltc autlivt* -^"tk* j^otHon ^t Is ^vi(i siwilar- 
JDYo «/(<<€ dl -for bs/ evtcl^f ^MjfiOAS . THe skeaf X-I^^a^O,ai^ 

wo^kou!| Ikam** 4^^- en^iite^ , etc. 

ea;^<:?lolal •'forms , -fifl. S^/i wfitkoic-f u'iiniJi niu^k vjuire K-coi^fW, 

eonltjuu \v^UOtv»^i\u yotaiu^ ^ a.n»6-»u> ait ita^e>^oVc(al ^ti«.s 
(riA-s *^.<H'icfU-8 o-^. ffu26« ^^T^yeA^idW t^dUsi OY* at ike laufpt 

282. I-BfAM «f UNIFORM StR^NSTH.S^, 

yort arid loflui Sawig a<) fn tKe ^rereJlng 9. Pig.286.lwet 
-Jor fi'A values of iL . Goneiiertng ^/( iH)Utfs of P <xi^ ft^^ty (>v*< 

cJdouI n) Since 



1-iQS. i^ ?c '.0 ^(jii To-(ote >. U7_ _ .„___m_^ll<'J5? 





F.^. a'?! c» 5a<fo 




4-2551 O 




♦ Kq, 213 







>«'g.3?6' §a?3 



283. -RECTA^G. SFCfloK. HElSHJ Coa/'stAIv'T. 
Two SUPPOBTS(^T£XTKtW»TlfiS), SlKC^^h ECCgA/- 
TF^IC LOAD. F.ij.2.8'?. T> an<^ li or* fre aunens ions •|lf'« 
sertion at "B . ■WTiHi "BO -free we Have 

t-B^a ^-pi-0 /. K= 1^ O) 

3 
Atatw oUier Section onT^O, as n.,w)ht-v£ ftie M/('d!ii ts u, ,ft€ 
VAvTaVie (/lAiose-relaTIan lb K IS re^uire«i j-weKowf foKmO -|yf« 

£>IKev scct*««^ ^ ^ on BO J Bie h€;i<j'ht V Ovid widrtr U. y<».v*e 1Ut va- 
Y*«i>)€S wHoS€ relatovt to U desiredt jih4 t^ Ky l^^ltieSfS are Con 
vufcfe^ % IV^ relaUV, t^.^.^tllt ..^.^— (l) 
^iVue IKe secUon at n iS a rect«^^^ SitrtiU)- t3llni^(at3^ 
F«r5i.e H H 80 -h, = ^^o^o - (^) 

x.^f 5-(i-)'=(i>^yf --(^3 

e^fescit^ tb X i:^.^ <JYtirnAre ~i? • i\£.^ cf Hi* tc^^er cu^-ve 
of )t\e ou»i>te c-l ttie Ccys\y%\ \o^^\is^Ailnal verticq'/ >Uhe 



^^f^f FLEXURE .Btams J Unif. =,\^^^^, ' ' « 



Vcif wtii cut ociX a Cuvv^ Cx *^^carWv £ff v«hi,'li ( i^ctted Une i3 Oj) 
!,a. .„ .^unWn ^ ^ ^^^ (^ifS ('6 J 

*n^4it s^ ^t Vtei^V^t orwi vA^i^i^ must v£ir3 ens ^€ cuise rooi <^ ,4>e 
^iSlbnce frr^TV* Ike. 5u^^t. TV?^ ^iRin CB W4i? we cCTT€*^x>ta- 

\lf ft»e l>£axvim ft\«S ]5v<?ljWm «f» li> ria»e cvtCuWy cress- vc— 

296.UK\roRM kOAl). TWOEMB SUPPORTS. Rec 
TAN^ULAR eg. SECTiOKS. WlliTH CONSTANT. K©w 

= ^ V» ^ "a^^- ^ *^^ cross section irt^tWe vw^^IVt i:t. jbTs^^ 
(^$a»»»e CIS tKat at tSie mtiJU^ie) ood ikc "het^W «=: i^, vArlofele . 
S(VkovhS. )e Oj^or^e^rec Uj^y ??0, g^ives 

Dxit to W a bectm o^ usriijoyrif'. drevi^fk^ Is I& to b4 «=-}* <?^53 
C<Jm}>tARfiL ^yrv S.(movM.^ "%«: for iW 4Tte.yc^y ^^ 30 

tfc«Tv€ C80 J sUowi \t to Ic «v^ cU»\>se s*i^ «t'^-^) ^^ ^"^^ 4 
(^ Wi€T curves ji.€^< fee <rorv»^Uie ouHine, of lti€ curve CQCB^ 



'wvhi-?i?ct$ In F?"<?s. .fgx, ?aa- r~;?;7i ; ►•*. 



ea ^«^«s 4 , I'^^ Y"^'^ '^^ ^ ^«WU 4 Wan, n*,Wo^. 




Sm^k en4 W /f, u). ?3 fl lA -^ , /o 






B«tti «?HUm*e4 






Hot. oulUnC- fw^ C '^ -'^ C 

TTTj- r- - -r- _. ^ ' 8S « 7«W«) 







^2ifCf pjTAMS OF UHIFORM jSlREH&Tti- lHO 
cjltuwAiiidL mdUuc cjWen,io cow$.tlt«ie -Ihem.** bodies cf 
s|f««i][UA cliomfcter, ide t<»ll6^hu5 ifvia^^ be stoic^i ikd 

noTWdd sW«»* UviVi£ &ui€v XU^tes. 
DEFLECTION OF BEAMS 

OF UNIFORM STRENGTH. 

2(|0. C/ISE OF §a83,+Kc flbukU wt<i<5e,bii+-*>^m^ 
>%^e'Wtcal ,U. Ij-lo^i:^ * ^^* ^V ^^^^ ^^ *^^^^ 

•Wife >\^ot\icut ot +ke gtret^ C6u)0$ ,«€^ €^$« (j6r) {6} a«ici(?J 
S§JWC} a>iiiil3l) o[ fkit vito^t dkiYECt s^wice iVciU.W- 
tWlmv^ Ha {^tm o( i<\e ekitrii^ cutv^ OB , vwlilck Is ^'^m- 
"vifieiriftxl jCMfvA K(w cx.coYw.moii Ww^ekd tft B , wl^k -Hie cuyw 

froM^ v^hicJi all vaiiabl^ have (iWoL|?^«(3Lye<l m iiie le{f Iiam^ 

KiKvubeti utp it Constant, twe t^xme at oil i^itiH 

^t-Hie eUsHe eicir^t, Wcuee Hve UiHer U *Hi€ dure df a cir- 
cle, U«Luli%^ a. kofls-ovk^ +avv^eK+ (tt B. 

To |eudl -H\<» cU^UctiCitjd, at B , covtsiaetr Ftcj. Z(\^ 



§ a<? BEAMS OF UNI FORM SJaEMfiTH. I ZI 
vvKerc d=: KB , <x>td -Hie -tuU chelc of VAaiu.^ Bh '-^-j i» 

av^ol .'. KB :^r. Oh '. TS 

Bv.1- OB = jl,KB:rcl ana Y8=2jo 

same ^^vcUvioi but |D^'bnt<rii e (j?ayalUlo|5ilD6.<^.icAl hti^tis 
sA^^Cj) K^vilwA +\\a so^\if>e dUuevis'tons , b and K^ <xi etii ^<?c~ 
Hovis cx-^ od md YiucWie , dlc-f lec1::5 an amotcwt 

^^ ^' "^^ "SVp ^^^^* ottood P iw tlie imdoifp 
£>|-tUt^ ^baw* Hewec +k€ IfliljeYUu:^ b«edm o-j^ flie }irest?Mt 

i?^K CASF OF^^SI (PARABOUC BODY) WITH 
Ij::!^ ,i,€. SYMMETRICAL. ?i(^X(\^ . Re^^atr^a^k 
^'AortiOK o|- tit€ iieu+Tai li>^€ 06C. Fcm Hte^. -free \>oi^ wO 

(ij^* b made vte^'^lMC b^ts^u^-se d^^ -f dx^ U Vie^<t^iv«, 

Now c-f ilie beawi wer^ ji?Vi^M\<l^<c^ T, fkeV\oineut of 

taknvi:^ 'Hv^ X -auK-dle>'lva4iV/? t.f (?ach mewber of (l j^aini 



§J2<?/ BEAMS OF UI^|P<?ftlv(ST/g£NaTH- IZZ 

To y)Wt •^liis \H+o +li« |cTii> C(»wtx4t^ i=fitnc.of(?L), 
we iteedC oul^ dlvtd* -WwowiK b\^ jc^j^avmC *<^' l.-evitt^ 

W^ <iA*^ >*»w 4(1^6 ^^^ > - (Mcii-(imva.Hv6 of eoclx hxjiu- 
(3* & , wbe« X =.;;^l J -Hi* slo|)« d>j — <ix f« ^«vo 

(C^-0 St'VveC -j^r X:::0 jVJcrO). VV« mdAj 1^0W ^(\ui ik^ 

dLwi U +wtc€ OS cjtea.i' £beU\<:j -•2.;5fgtktJ ^*^ ^^ ^^^ 



§S,n BEm^ Of UNIFORM STR^NdTH^ I2B 

^(jwsT-dui vvtd4k=^bj buV -fk^ htXaUi- h c^in-^^tini^ov^'r Ute^- 

h. at >H\(ic^|>av\ . Tkt d<>Kvtr<»eHC^ o|^iiv<i iwo 4rui%ca"k<ji 
vv/e4(^c6 f<inrSfnvH^ VV\€ nUcUte (?u<w^^ o{ liu heavi^ Is u\ek 

awdL |>t<3tdHo (3l^\mqU l<>^fi/2| ^^ Te<^utre^i4o -^wi live e- 

tie auXv€4 CB, (i-vui B,B j axxA. -fiwodlvi tlui def (ecHoh. 
Tke toltciirK^ o| +Uts aiidtUe -folio w<n<i br^ Mem cu^ 

KeYe qWevv h vvoV owe o-f uvii'|or>n e'Wft'v\<:j+K. 

2q6, SPECIAL PftOBlEM (JT). Fi^. 2^5". R^^^uWe^ 

CHAP. !3Zr. Flexure of Pmmcrf:ic 
Beams iL\\det OBLIQUE FORCES. 

bi^t- •tft^-ee. ^^kvviAl -forces will b«. (j^Yv|<Hfl<i "te £?we [jIau^^ 
cialjledt. *Hi« ^rc^-j^l(3w^€ 5Vuklck coukivu ilte o-m o| 4iv6 b^u 

(\Miuee(3L bvj Hiteee ^Y^yy:)i 'favces will cu Uj^rg' ts^ (5«m- 

Hve bcoYw \nUI Ue "Hreaic^ o^ uHck<XK<2j6<il t>^ Ike -fl^Jvurc. 
H w'ltl be TememberCflt +k(i:* ^^^. jarcuiov.^ (mji^lmii?. tiu« 

tkvtju^k VH 6^v.We a| cjToviK , ve-si-edl ovv 4k«, |(3^<!t tk*d v/h^ 
ix[v.^vivo\\ 0^ -Htc bj2<x^r^ k^vvv^ a <:jlve^^ ^'ecdtoKfXS one c^ 
in laci<.wdLt\u} su.<'^c€e t^ o^K^(d«re<i fr£€ Ike coid'i^UH 



^^ 



L, AJ ' 

A 







§ i?^6: y^ -i?>^^->r'^ 



R 



§Z^A ^ OBLI QUE FORCES. /^f 

luA^'oclue^ awvj o-f 4ke ejcferWl -forces, sm^e 4(^«e iw tii€ 
joroMevws Ye^l^Nnred^it) , w<we ~1 "to +lt« beam; bai- U^ 
'^kc. ^Tofcl«viv$ o| "Hie )pr^9&^ cluV^W di^ck U ko1 iite 

tvx. -^(K-t Nnoui Kov^ ov^X"^ (xv< yde^ ^ oeo*m€rn^<sXyC^)c\if€yijce, 
^^ves vwWine ev^ifi ctx^ to^)yo^eci m (t-^WeiA. «ecttoH ^naviail 

-hr<xl a-Kv^ inaWc^ o| +U ivcuivoJl oris itself, gluce 4k;s 

5a^, Ci^ASSIFlCATlON OF THE. ELASTIC 
rOR'CBS. 3KE/iR , THRUST , AHO ^TKES^ - 
COUPLE.. Fi<]^fiq6^ U+- AkM k ^h€ e^-e^^uixi 

d^H obUc^tA^ ^ttes . C is rkd eei^lr^e el qr^\\^ of 'f'^c 
aeciiov^ eK-lsfl^e^i , av^i fiC "^^^ ^rtxv\W o-vi^ *! 'fc? -Ike 
|0T(M l:^!^^^ CAk. Tke ^'(r^ste^ dxrK>wa oic'tic ele^i^hi? 
(7t ctjfux ( fcJAck ~ dFj of tke '3ecHpK. c^\a.iU1' erf skean 
(yvku^€ QiiLm -r^ J ^ +(i^ •* ^-o-tul ^k^jW ''j Iv. +k« j^tUn^ t-tikt 

tiv'e/sse^ booroJXcl io A K cwJL bro J3orHcH{»l ker i-uhH of 
ar«A. It3 4k^ dlU'kucee^ of fke dF'^s ou wkiek l-kc^^ cid- 



%2q5 OBUaVE FORCES- 125 

[olv -|<at*^v€. iiv.es € sHc^ses aVe ail fi| ck€ kt%ui ^ ad Ivh- 
•siov. crc all coVM.]ar€J&^oK • bwf ;-^ Hcc Heichra.1 (Wia ocetos 
wHklw tii<2 U\M.vb of Hve s£xrKcm fUev^ wilt b^ o~f cj^jxr 

^vW kiwis OV*. +l<-€. 4vvo si<i«3 0| NC'^_3 TttVOl«^k C V^i^ 

U i W eecHcvH i^seLf; ii will (itvidi<i +i^€ sfres^ -in.V^isi'Kj 
AA' iw^ "fv\'o j&cvrb p, c^-M |3^ , aA<i will <>Kairk u,s fo ex- 
fa vc^^ "H^e stress- Ik W-vsits itvf , 0"k olmm dP at a ciCs- 
i-avLce -^ fA'o\n -fke g^BLy l ^ ^viq GC ^ iu. 4wvo j^oirfs; cni^ 
|5avi -HvQ ^Obvtve -f-or all cif^'s , Ihe o%tT <^ej>«iident on 7:^', 

fact-al norma] sFress (m an^ <^ f\^ "J^i ^ ^ 1 1- ]^5^ ^ - ' VV 

For exatn^le {Vie. sW*:>5-irili)^5»1y {5n t^e ^ttre dt T., wKsve 
z^ ~e^ ^ wV)'^ be *]^, ^ * — - "ho ^ ^^^^ 't 1$ now s^e\i Uc^ we 
iT^ay find ti'>e sTveSi at Ony (JF wK^c* Ip, ^*'*^ K 
have: Wen f<>ar»cl . !"[ Hie. 4«s^ance a ^ T^^TvA/een llie neutral 
andi c^raVi^y axes is cie^iviici ^ vve V\o«ve Vy 5ifntlar"trja«i/ieS 
]^^:e .*: C'C^ t a. vot>evife ^c ^-6 O) 

It k. new reaa,ly S^e^^ c^ya^j^icall y JKal jki^. sTr^ss^ ov eW 
^-.ralia l^lan^ AMT and A^' M^^ T'l co.sKD.le a u.^^ 
Uie " ur7;{t,rmTHRUST*>r 5»\>.piy lU THRdST ("rrv 



§£^5- OBLIQUE FORCES tZ6 

J I i^ also evfclcu't •ik(rt +i\€ j^Vilvv^ rvtUs'-c<?|ob |cYm- 

— /4'M^T' , It will be ^kowm 4ita+ 'Wie^ « cjrou^edC d^^s- 
e^c^vvsKKti* a ^'STRESS C}0UPIZ'\ 

In o(ea(iYu:f v/viHt +lic fre< bodi*^ KAM P{(|. A^4$ ,vv^ 

a($o t(u?e€ *7 io ^^e be^xm 5<xiwjt a.($^ $avvi tit^Y mc- 
\nc:Htl^ ab^i some^^ "^ "HtUc -fiste^ |pt^we . ti^ Ht^s 
aKiS d)-f rvK?rn^wt$ fa€ (3LC ^k^ {vc<^l\^^ -<Xfi^ o^ f(i.€ 3«?<;* 

to tUe (3^<uu <jiv<<i X "1 +0 iH. L^i u^s $ee v^rfl^i" kuxr't 

3e<? r^cj. 5(^7, wlticK cjWe3 weve^^ aeU^ view. Refer- 
Yivu^ h e^. (A) }/u^ s€«? f(ujct g 

[see e^-C^) §22] But as-tW x.'s are me*6ux-d<i 
^rovw (k a- flmvUN avis 5 mv*-«+ be xe>rp. H^mw 
L n J. ~ /*^^f T«BUSTl/M 

D-ke SIX of eiA*H«fT^*3=t',F = { ^^ p(jL.L r^ 

/4Uo. 

vvlvilc tor juOMtew+s aboict <i ^ee 6<J. (./Jj 



T-r: . •%■ r. \.,«ii... .f..i.. f re..' ct 






ik^ 



OF THE STRESS COUPLe\ ii}4e>i ^iaMivj:^^ bvj nW€t?> cm.- 
i).\^ e4v^ivalevvt« TM- 4kei€ ^M«dl ^+Te$^^^ <*^e eauAvd- 
•'^^v: J^" -te'fce.^ +kes^ dc noV aMipi^ m £4*4>"^^^*' 2S , 

^.•( HvvC <!cv^iT«^ViOTA.^ \~^J ^^^ iiA. +k(\t sci 0^ yxt^n\\:\ 

>.f^in€ ^^AiDfVK. 5.-$ WA5 U4^/^ ivv -^OVWv ^Uxwte fcrM^lCkj^. 
H'C>.:\.<\.1 itJrt^i^ is. ba^av^C^/i bv \ke iWuJ^ d\ ^ll^ +k^^c 1 



rii^ iQUATtON FOR SAFE k6ADtNG,-H<eu,vaft 

6r r u r ^ R' — -^ (7) 

j^^S^a. HkASTiC CURVE Wrt» ©SUAE FORCES. 

(&vj eU'i'fic 6urv< If HOW ♦it#4lit -ttw. i$6uA s^ ^\m. iieKlr^? 

(9^ ^vlILj , v«(Uj^« «^«^, 6H*tK« i|v«rt l^^-rita (=:obc) o| |ib€3 
S^ 7 ^ f^ ^4,+ e^|Ufltl^ bNj all 5 ikt t<5c<xKo\i. 6| tli€ eeai"^-! 
t^ woutA be 6^ de4€!rmt3%€ii fe^ ike $4te$« edible (sicyta^ 
KeiMil 4t? ike cUt^^es ]pYt>dLuci>ii:^ ikem , if Ike l^ce^ ^^ 

mAiirv u,vi^KAw«jc(i d*tA ike t«(»A4HieKi^ <ma4, skafHulu^ 






^% 59 6 to 2^% 








3q3 




^etvS, 



Inn 









12/ ^0 g. FLEXURE-O Bti^UE F ORCES. Uq 
s^ (/CQ'lJ aaA (x^R! vvQwVdl ^^ 'tW, toA{\a^- t)f-e<trvaW<t. But 

iivv i^f^#^vef b«Vwe^K £lpR OMdl (Jo*^' f^ v^^ «>>ux.UjkiH^ 

ivcW vsi^ e^ iUe, vs.vvUornH bull vverx as kcqk 03 Z2 OOO 
lU. jtjer ^cj. lu. r^€€ 3 205J &^& w<?4i ^Ct^acl (i^G: bs' 

Vke ^v^'vw 0^- S\\^ vyvOmeHb oj^ Hie erWrvioLl jotc.«sj hence l^r 
-vHuicdlt beams vcv^^f ofaU<\u^ -^iree*, wewcj^v^ sHll w^e 

610 -^ ; 0) 

'■xt ci-we J^nvi -for W Z (;^Hom'^.) O^VUe ek<&Hc ^^^•.e^ 

i!c]d. OBLIQUE CANTILEVER WITH TERMINAL 
LOAD. Pt^. 2,^8. Tkc "^Vfwo^*^ o^ i4u. icm^ar e^^of 

t^OA avui i>T ^ ->^ «nvo^ , Hk€ k^v^i^Hv o-f-tUe ^«rJ3^{rt.-- 

\im*.d +t> Act. [^I-f- i5( vA/er€ v«r\j smixU ^i;\owaver ^ ii u ^^l- 
i^e -^fejcj^Yi. (i^jLu^C'^ ^ H^v^i Wad J 



ilu^^ca^Mc^ ^mc^vAlok (see e^^3 (A) , (6~) , and (6)) \k7 e'^ 
Ux^i{e JDYct^ of tUe fiedien ci?i^^4r::icl aske^r J, yuko^^ 

y^he^ct * X-. p smo( ■ (/] 

(iiiinHS^^):^0 or 

Von. O^L /Pic,, 2^ a) , ,ai^^ iUa jo^ , -m.e dye<>^-mkK- ' 
s(Kj ucHv^. ouHx |i,loT€,^ (<xU -Has b e.om(3r^s:uon {| e --no' 

X, \iPj^e +ke m(X;K. of [jo^ f |)^] vA/ul be uxlU towff wkf 
(<'bT€ at L wU^ve X is rc (^re^i- as |oogs\bW, -:l ] /.it J u^^^K 

»itox 
H,i^>v^.^llvj t'A+ke tr^^r ^ifcve§ AlciKflj iU ubjp^.Y aiae eftfitf 

erf- Hv^? vA^Jo ^f ^.wd H«(xv 0^ Sine* ikfitc |p^ is smcUl , x b«i*«] 

. d'ievv VHOAj be ^u.Kd(be-f0t€- re<xekmc( ike ^ ^.^cint )iA(k€^. 
' 1^2.' t^f ^^^^ wlxetre etKs<3(}tAfinVlvj it^ dtctis m lite vtA^ 



^i(?<?Ui?vv p^^^^'S iiivyix^k fk^^ oi^€v fibre. I m Ajiv section 
abi;=ve. +1^ § teflon +ke vit^^Vral (X^^is is on-a^^^UvavM ue. v^ 

iAfW\ie OL ^^e cxxU oj "Hv^l beo^^i U tke U6tcs o| tit€ 
c^fvc'* lA.i'ulev UcxuLve, 4s olveitciM siuW, fi^w<'\/€<;tk<' 

.^<?xv?e ^ke (evev-^arvw LR o[ P ob^uf J^ 4o be ax^^i- 
ev bu 10 j^^vcevd. tkcK iH vd(u€ (::= l$iHo() hi'ft^e f^ 

TItC dt£.^t<2<.+tOK OC \Y0Ua, ikn Wu3l€U.i oA k^ ^M § 

iWeU^ , pi^\H<:| P s>iV a ^|<^ +k^ P o| fU}. iUq ; but 

P6osc5( ^ II To the •favoj^ev.i' cd- L, ol lever axy^^oMA 

3e<t.Uovt?i3wiwn€<?^!E (vtu)Kis,,)"^0 w^ k^'U'e ^ (more e?c- 
(jurHv^ tkAK |rom c^. (.3) vAiUcK x- t) 

(iA'V, Kaiv'e k^^ eKJoJDo^edL P re)^Uce(i bM ib cc\MboH€»ib 
ti oaaA "7 ^ Hvc ^>ce<i -kuuj^ cd: L ^ee Fvcj.30l). 
Bui evevi.(6) wiit not mve an c^caci uaX^^e |o\ -fo^ a+ Lj 

ovv ctcooiA-vcS: o\^ Hve ^Tet?eHC€ avi4 !-f'VCV<xj:^e &t Pc^ol it- 
ivA-^ . ITke Iywc yoliA-e o^ dl iu Hvi^ cas^ vwavj bi^ obhuv- 
ed ^^^ ix wvd-vtocs so><U<xv \v Hied iwdtcaiedi ch \ke next 



If 



^2 q6 FL^XURL OBLIQUE FORdH /3^ 

if 7. CLASTIC Oil^VC OF CBUQ.UC CAHTlU 
Vt'R'wiTH TERMllVALLOAD. MOHL tXACJ SO- 
LUTION. Fov \{CKxlt\r^ ^)^4ce ii^e c^Ktilev^v a.^ va 

■teaee Ike vywn^ievc' o| P s?JUut -ike c^t^^^cv^ a^u o|(>.^t^ 

^v^ ?>Y ^^ b€/«tu\ » For a -^f^ ^^ On , h Wwu^ du^ 

l^e^ ^v W ^.tQ^^cij Ik ^\s 64u<3cKi>v^. ike ytc^kt rum4 
number Is evldeniUj ($€c -ft<^. 5^^ <xvu^i3dw€ qwArrtvtv^; 
~^WW l^ (X^ IV should U 5 -(oT EI ^' -^-t3L?c'^ t$ n^ccHv€ 

mu-i , (it y^M^- b€, vM^ IktfV- -rtv^ <X;hsX Is (xlvycxvjQ -h 

X^ ^klftkv £^ ^eMx^Ve^-Hte NApefSlAN BASE ^5,7i5i^^ 
-k'pCC^cy. '7-- £1 



^.- '/wivkk e - (cit^bM^ tff ouf^rftWe from Hie ^vavH^^ 

Hr.v,- C2.) jU.;, <fe(;4J iwlU f^:|<3ye^<iicH ^: 
;■ -M.. UAvk^ic^ovA/n ^uaw.i{-K^^ caw. oHi^ b<i cLcc<>m^ii«fe;.a b.. 
/2^5, INCLINED )^Um WiTti HiNAt AT om END, 

vv'hU iWt o|- lie W.>m^£^|?Ih b«4.w^ ^AHkvu>w!^. b^lrkiw a- 

owb^^. Subp^miA ^Kir -|<exw.<€ «U^kV wi ^i^c<i ^it^^e e^^.- 
"-' (-»nc<^ \u.-VW€ fUMrtA.^ n^xw-wtf oii i-w P'^'ob. / §37. k{ 

p ' p 

fcuci j-Olr Virt. "VWyus t" '=^ h p ~ H Co'^^> 







> , I. L T3 r cot 'X z e 1 

Cn' ,(10. dC^ . rU^AK |tx)vk E (i£M/|iHii.ani-tf;x) 

(iWc iiiricii -:::-) f:> P 5- V; siHr>< ^ M^ cos oc ,', 

rr. . ' ■ 



*»*^^ . ^^r 3 f- jif> 



6) 



( -^ ..... u T> / / 4 

H^ce (f^, -^-f^) -for ^ecftft-u,s ouCe ^? qr<^^e<i- v^^koi. .' 

J ~' V^ co$ o< '- Ho ^i>vo( - y P cos cx ( / V / 

c-^ (|>, i '|?jj ^U'^q tk^ beam. Pack .'^rduiak i^ hU^i 







A A /fA 




Fc^.3o8 



% 300 




Rouni «r\<is 



raninc?:; 



ii^ 



^ 



A 
B/.i 






er<4s 




U J 

} all Ax^ 



Ri^.3/0 




mr 



sn 



JJIW^ 





,iJ<UHS- . pgAJi. 



^■iCi^^oS. Le^ tk^ btam bt c\ v'/y^u(^ki uciv , the |o{!vt 
p ■- 1800 tb-s. KoM^lw^ -frcm VUe m't<^4<^ • C^i^"^^^ ■;i<^«itn.v 

£v Itt^v^c^: aUo ^Vi€ wtax. hM ^[tocjc . 

^:^^cCuA^i{^^i^) P'^-lSOO Lbs,] F ~ 5^<^» m.; ^ ^ .• ^ 

V;|j€i Du1ci( |ibre clos^ Lcvvde^ 6- In tSt^ icwcr rut'^^ fib^*^^ 
•?i?« -J.^-. r.vcK , ( It U here 6u[3J.}{?i-i^ci tl-.a-t Mi«s: bcAv.t r.j ;^'' 
'3i)0. STRENGTH OF" HOOKS, ./ivi £?rdtvtaYV| iu^K. 



6 

f, 



it > Ui^t^ /^CiA-vvi:y:i 'i'>.<*i *. (, .wid tkoi five )n<i.x^ 



§5pO _,". f L U X U K L. .O.4L licjU l:. ! C N L t:. - L5.6 

CHAP.V! FLEXURE 

£)F.\ONa COLUMN sr 

365. DEFlNlTiaNS. Bi) '^lon^ colunm*' i^ vnauvl 

% iwc cc^^4pxt:s3iV'<i' k'TC'C$ , one ai eAcMi eA-i^eiHilM . aiidv^heiC; 

w^w, (oY ^''fviU'') b\j bucKUu<3| $.ldew^\\-a ji.e.bMj |(f^xuvv ,V;-i;sh:Aci 

<u;'lu-mHS K€e<i iw buUdoA<:js , Hie trnix'^Test^iow ^MQW-^bQ^ts 
C'f bvldiije "Ww^sts and xu/;^s,avid. Hie^lieKH*' ut a Kc-sf.U^ 
Vio^k (it^ Ike 'pviViclj^M f)meHc<^l ^7cavv\]:>lC'6 cj (uuq ef(u)>iiis, 
Tkai Hu^ skotvid be vvcak^fr iltdvv sltOMi bie^cks o-^ H't<; ;-jc:tH4-« 

eats-gfv 0^ ?-l«vu'^£ J exj:)eYiv\a.€Hi b«.\'vi(:j vc^*^ iavc^ets relied ni 
30 5. END CONDITIONS, The shou|1K cf acaiu^^H 

lu^vuu KOUNP ENDS; lu iU (aH^v o<i Koi/hMi i- tX^; D 
E!\0<.(.^r ri./lT BASES, cv S^UAhE ENDBV 



^30:i FLLXUf? t . u Om COLVN\U^> /.37.. 

c^ cud ccvvdUtDits \$. D^i-civi^bcKfi^^ r^ as ^"^ PIH AND 
SQUARED 

ax^ faeivvc^^ vwvcck -ewuja^rakdi , I-f ^U€ tT>UvvAtvu| o^ Hie *- ■ 
■A,^ \kels ex1ve^ili€$ ^ Ml 4 doiunvn is k be ei;v^«bl dered a^ '^ouicl^ 

Tke ''S'^torrt«v4 of tw^Ka** c|tk€s^cit()u o\ a. c^UmtVi vm\\\ 

305. EULER'S FORMULA. Tak'm^ H.« co^^ ^f 
ct Tv^wii ' e v-vd^ cctutviin, Fic^» 313, tita^i^me ike i>*icWU 
vi^ ike ievu|Hi o^ aw oric^m , \nUW Hv« <xvU^ fe'vvM^evcV it> 

■:Ut^ -VWi- wiVW ^A.s tioVaHDw tke a)cU IK viiMsi b<L U 
Iv ike feeavR ^ct^ivi ike fK^uVt (313). C^K^ideriMx:^ ike 
fv$f bcdv^ nC 5 v^/«? ru>H %ai Uie ske^w U :tCTO, tk*x' 






tM^ „EU.XU/tJ:: . LONd COLUMMS. ipj 

•^5A.b^o$e tV v^frlH^wnif |^r ecuiit iki^fvvf f vc-iu whin 
C)Kxd Kj cr Njj [dt^C F t«:|, 314) ^U^44i^ SNtit^ Hcfi SiVrK of ^ 



5 UC 






^I.^-xPa,-P^ ^^) 






JEL . d\ [El dd) 

(<5j f5 fk^ &<)maHc>k i>-{ rtt^ ei&tHt <^Mii POC pe^j. -^^is 
c^\v<M \^ (xiM, be 04r.wj5ia<id for a.^\v$vL x oW wl6« wer$^?^ 
fiiA^fif'ot^a a h^ (U^^oM^. uvi P, f-ot m «ij, {bj wk^ii^ ^ - i'^ 






I 



\ 



f ,c(5. 3 16 to 3a ( % ia^ y. 13? § %/ios ^« *'^ 






\' ^ 1; R 




^367 



P\ate4 OA^' Atii^l*^ 



PJ//Mt!^97Str/JlgMW\ 



fj^. Sao 3^^ 



S3tl 



FI3.321 fta«' 






■ cAUKJi. LONu CCLuMl^j..> 



C t ! 



S = Elir 0^' 



^W^edl eolvun^-^ U\ ^^. 315} wHick wlU h^. tke. ^Mu^vn ci'i ah\^ 
I\\ t)\4€^ wc\rei•^^ l^ riv<?. ^T« \?i 'CSC, ilvoH t\ i-u? 54^yivV€. (*J^ 

b^ c.«?.t4H>u* lx. 'i^ovwvvvavti jarC^^ lore wiVk -^K^ lux.vi.cl ck ii\€ t<.b|:>^-v 

ikn ffo.Qiu c<;'.('^j VHd^^ lo«. looke<i. u|.'ok d^o o^m\\^ iite BREAK- 
ING. Load i»( a coI\a)4i^v w^U roivvui e-mkj avH^- 1"^ caU^cI 

Rj^feft*.%^ wow io Fiq. 511 ^ li vviU bes£€K4iu^ i^ ihc ^Vw.:^ 
X ^^^ 5 15" , Vtv«?. -^incf.'s 'uHv\.C| wUl be as M've^r-o s,iw?>ivn, v/x ' 

•^hc |nclievi'ta-a ci auk -blocks cu^ qtcules /vviu^^K av£- vwiT^^ disced 
'-erf >iv..j^-l^ (XA > iUs^jfcVuTav VHe'tUod o\ \:ixty^!^\^i\\c^ ik^ e-u^cU 
{ho\s\ Vv^*v'.vvi(^ , fnd d-o ucr VTd-<^'< -^€<'c v-vUii vvvKcaI {(reecic-v^v] CA 






-1:!£^ tJ:£2<M£_Jd)liG^C^iJJ}/^iS^ ^//C 



i -. 



aads 



^.ijiiiis^^tl 



i 



Tke^t^ ^i\-Hos cue Ati- 



au^ 0^3 J ^^^-^ tcMU^.ftd cx^ ^iviwf^ >k€ Wii^k'tK^, load t^', 

^\rt<KH^ (evft (uux H^u,g qawec^ fcrf ikcl^ . iv^ ^ke C!e.uUU.. 

.. i^^/€<a^^ cf- Vkv. (cad. aN^a H.^ ^aa:iU -.ccK^.h . bio ,A.lk' 
. e()U^u,. tlvt U^r oi<'y\^ of Hif lixxa about \W nua^f^Kov^r- 

50A.;:/ AMPLE.. Euier'. ftiVWiuU it ChUj aj.K^...nak 



. V^^'^Vy^^^f? } \! 



V)Q<{ 



■'."O K V'vH . 



\^ aw QuX\n\i.v ti ik un 



vvH^c ew^S <\>f^ frt>^: Vc fuxn . f4«4^^< v-vi u^?«' H%6, xx>v,^Uu^. 
l~-3Q0OCOpO i)cn.,. ^v s^.lv.4:.K. The ciXvy^^^ivxx^ 

J - /;i ^^^ - fn A ^A^Jj^J r: -f-f^XY' \i\C^M^i. I'Kek^.n . 

305. HODGKmSCN^ FORMUUH FDR COiUWfe, 

vu^>k a.c:j64^c^al fbYv-v (; ( fe^jm^'S u;u for b^^<lka^^ ioe^d, ii- 
^*pDK 6ci4M*v«Hs o( Itoh and itH-vtier, 

VtA^e^^i :xs Mcc ^qwNfie of Hv<j Uk^^^. But W-odt^ ki v.s ^v^^ ^.x- 

P. ^- /-a Tr E.-'F 



■^-(c<-u.1)a|. " "^ 

bi>vwi?in& dl|((f' ^(4<|HK^ jfcvu Hiosje- t>t E^^ei^, 
Heocjkn^soW'? -forwAuia*. cut as fclUws .• 

Bn'^rtv^;^ load (H TONS) ,^ , v/^ . \3«^^\ ' ^ 

'Pov :icUd scf^tarf cotuvi^ e{ cItv| ogk ^ f_lAi;^.giiifo 
-/ S\ ^A ki v^<^ U<x4 \ v\ TO N ^1 i; 

rPcr s>;tld sqwuc ooUnu\^ o\ dfv^ {(V , { 1 gi - e^Kc^-^ 

d^;.v-, .:ovwcc v^lvx-i ik« 4t^niK<3) c^ Vke eutis . Tke^c -fdTWu^.;.>c , 
(!v^. vvku.U cl ai*^ b devtok -fde dUwuLkr ouv«.d wicUK, ai^^ 

form J iWt. i.vvuv'^ fc 1^€' frw<J]pU)\^€.d oxt^ ^Jaeoiftt^. /i<r ih. 
• ■v*.i^Hv<» b^ctx^vQ. •siualUv H^e vatu.t of Ike bredkivtA Uft<:( iv 



%7505 FLLXURE. LOH& COL UMNS- ,._, 1^:1 

Ih ^i^ck a c^e fu ^.x H coUvi^ ^ SHORT OOtUMN', 
and tk,<: Vdtiiv^. PC isH be -hMea OS \W b^eA>tH*<3| bcic(, ll^'i^ 

i-<:.,1ke bY€^Vv\vvc^ Uowi is Hte-^ui^U*' ^| five fwo wu^:.'?, Ft' 

pf 2^,4^ lbs, e<xi:J. J '^'C<>H..1./ - ^f .^ ^^^^rn 
^•♦A. vvK=vd\ "^iv€ covv^V, ^>i^j6 |e< c-ci^V iVi)h,aud ^3//. for 
wvou^W , wvhVl« n X 1-7 fc^r &<x6V ire^v\ a^rl ^c X '\tx vvrou<|Ht 

3^6. EXAMPLES DP HOpfi.rof^ MI/LAB. 

?VC'V^ \;^\h tA-t^sd a^ a Uvv:\ <KJlwitivh ^ h^in^ <x^€vui|4k c^f Ti 

I.| w^ kujul recjAvd ^i'KvU&Lsi "b-W^ ^ec^m/voi ar^cv <y-f >>&M, 

M a3Vw«ri feUtk. (<n ^kovi Column) w<;^ ^kould KoA^e -^f ik 
ooM^i |:>ree^Ve loo^ a1 H-u eiAj«\l« Irnu^ (^^ee itU?(c^. § J103) 

iu^W" 3,6-5 



i 



A30 6 { L.i:zXUi\t..uoNa C^LUiVirvS.„/M 
[lo^. 3.00) X 3,6^5" ^ 0.47?/- .'Xa^^^-^^-z.^^f^?;/^ 

TKf. a'»Yr€^[3CiA-cltV<:\ nuntfej^* cvy€ 6 6~6 rxvt^. A^^f '-' ; 

::=337^0 lbs, 

tUa^v^ iV£ ii>000 Lb^. ofcfcUv\€(;f fttvi*^ fUe '*'^h^rt block *' ^c^v 

Vkiva y^ t\us i.e. , vYOwtxi he S2lO ib^. wk-Uc wHK jjiu-oiud- 
jauiXT^ €v\ct-OOvul\Hea^ , we sk<ji4ctut£ one K(Kl-f jDT ^Jl| 5"" lis^. 

\mt o( 3a'f>eVv\. Let dl --ik€ vwvkwcwv. diA-mefefv U«-iVi-c| fe 
^v^c-k^ locui, wklcK 10 4d be ^ix. M^me^ \k^ ^\\^ak -^eJl^e lead , iv> 



or 



71Vi^ ry^uVV t^ |0^ fto ^ud^. Xf ^^ ewds w«r^ YO«*vi- 

307, RANKINE'S FORMULA FOR COLUMNS^ 
Tkc forwv^U ii-f tkv5 VKXwvc (^omaH^^^^ cAl\£<i 8.t^^*^^ 
aUo) Vux> (X <^iw$ wW(?A vw^svc vaHovtol baa is -Hvx-vi EuXii^^j 



Viortlo^v ^lo\^ (P^* 3l6y^\H<i<' -five tVvtu*^ o^ti ^(^j^^-fi-^u, 

cfivu|j$,) :^4>). Here |>^ dtevcoU^ Mve ix^|tJYvt\ ^es^iAY-? 
(pv:r ifcv**t o( o.T'ea) dag +0 Hw«! t.cvU.|<?rw ^vi*>Bt,iUv<i jp^ 4W 
pt€^^iA<€ ^ Wv^i(rK(^^^Y u»v\iV t? ^ Off <^) tu 4iv« elc^fic 4^c^ 

|)lav\e 0^ |l€*vor€») o( tkc 5«eU(m* ■ Fl"? iK^ ]reM (kstCi o|tt^ 
Sjfmom^.^) nrO ^tv€^ Pctrr j[^ ^ _ ^?J 
i^ii^t^ P^-i < Pa vnVv\W. ^jI^iXKd r^do M^fc-kAA^i^e , 



: ■"■""^'-?^^=ft — ^, 

W« w\<^kf vvovM ftolve f^ P a.v»4 call if fke ,o^f< U^d, 
bid iVU ft^-ibwMirc^ H ]pr4*e,»d i^-ME |ormuJ& w<k-\oni,' 

v!olv€ -for P,-calt{vi^ lH4v<u -Hvft br«aktH<^ load. Now 

at: .-for J ji b«A\^o^ <x\K aOjs+roL^H- vvu/mUr <kt.\i«M&^\ tw 
vK^Jcnvwtva . \A/e vHdW( (xbo wii># , -ftrr to uy ftwt ewe . 
1~ Fk" , k bemei fke raoLiw oj! ejsjitiHftn (lee § 85"), 
HenJ« , fiw(xlt\j ,we li(w^c (roiv- ^.Q) 

B-.| tke same reo^eniH£| as in § 30 3 ,f«r arouwt-e.d~ 
«d &<;LtA4-i,K we. sKb'sHK^* 5.1 ^ I ; j^t ^ /sin- aH<3(- 

for «. r«t<H«(-ftv*derf coUwit) ~ 'o ~ 7+^/9 _^ ~ C^. 

f3r«ry>k(vx(j) Uixcl for ) FC 

vvlii wi<vv| Ht€Ye|€Y€ be used Im. iKcivv . 

u^tc: vvv Hte^^ ^Tvu,4xU€. Tkes€ are boL^^cd ou Hc<3((^ 



§ 307 



FLF-XURE'J nf^a rr>umU'^,. //r? 



{ 


Ca.^i X\o\x 


Wro'i 1-^c-u 


Tin\hi-r I 


C h\ [b^ }^x Sjj^in, 


80 OGO 


36 000 


5 

7^.00 


S (abstract nurnbat^ 


\ 1 
6^00 


f 
36000 


3000 



eKJbve^ed l^ S^. INCHES oovi^jI P m POUNDS. 
30^ . EKAmPUES , U13 M^ KANKiNE's^ FOf^iVULA. 

cVcs . WttU 4'^^S€ v<:xUc€s ; aW C! - 36 OOO (bs . [?<:^ 'i<:\.ni,. 
^^ i^Z7)<36O00 ^30 744j5 (b.. ^- cO 

/4~ -J 0^^)i ^. f^ 



2>6occ 



^\1.615] 



T^% b^%\<3j ii^^ breAk'iv^ Uxxd; "five ^^e (ocui wuxn^ b« 
iuk^vi z:-^ ov "^ o-f 3^7^5.6 tbs. , c>jOC^r%^ OS 4ii« 
>tii.4!HLf€ 0^ which Ike eoU\nY^ is a rn^^tnb^t is ,jwU$c^id 

• iV>s<r«C5 -^oT^vuxU 33 72,0 lb-5. was obVttxH^ Ous <5^ br<JaP- 
i.^-^, Uad Ik i^is cdsc (§ 506} . 

1^ ~/6/0C. lbs. a-s break, icc^ (Jl) 

H~'^'^^<C>d lbs, a^ bveok U^d /3) 



iw l^v^Hi , v\ii\H rDiA*wde<i enrls, Hul-{ tb s<^-^c loc»4 i^^sj 
fee ^Ix: loKc^ 4D\t5 ((.€ o^ JilUO tt^. <2<xck) Hkiv\<\ 6 <x$ 

"j^ cl^ , He^ce ^. C^~) q{ §30] beccv^es 

fiver i-W^ biqtv(xci Ya4vc e<^u^Hov\; 

5<?c}. KAD/I OF <iYf?AT(ON. Tke fdtcvviiMjk- 

^jidLiws of (\M^ raHev\ ' of fi\« qivevv cro^^ secVicn o-b^i 

b^ tive ^iAuiMiOtidiiHa>v« of- flie coIi4m.%ii. ; i»t. +kat tUe 
<Svui (err bt (k) U c5< [;?iK-joUc^ tk-c Coluv«^v\ >iva%j >i€W 

WW Am. ai^lAl jiilakui j:)A.s<i>^^ +kt^U;^U "Hie |3m ^ t f Mte 
bv Arii^« oj fk€ |3m A-^e ^rm , w Kite a^ r€<:yotrti3 -H**" 
UA-^lvv 0, j>iAjAt (>^)3i£,wuiicvvUr 4t) +ite Jsin c\ri^ xm^^d- 



§307 FLEXURE. LONG COLUMNS W. 

3n fte case of d iWux cell ,/llie value cj V* i^ stncUy Ivue 
{or rr\etal iivflmtely iKui •, 5Ml,i^ iliat llit'cktiess <ices not e^cce^ci 
*/g cj rt^e evVetior d/cimeter ^1V«C -jornt given t^ 5iiffic»^nUy ncay 






i<^= i^^' 


TUi K^cknijuUy Cell ^""'"^ 


^ " \x' •h + i, 






!^ '<'= « ^ 














At^<)le- ivou of 



uwe 






Cvo^s o{ e<{ttal ayiMS j 






earn as a l^illar. 



I-B 



r^ t 



'^ A-vB 



Channel 
Ire 

- A V."c=^liy 'h»if^n^ e<i^e of {Icin<je to ^id^^lc o^ web. 



, <^Vl^- ^] weio - J53 <7-J (Unices V -^ 



A§m FLEXURE. Ljj fi& ggiyMNS. /M 

3/0. BUILT C-OLUMNS. Tli^ '' t4mpre^-%m \nmkm'' 

^ko^v^ iVu rkj^, III- 

bc^k lt>SKe^ Wvj tUt T^WvvU e^H^flo^H ^^^ 4<>e i^ie |^K 
MoM^ dU^i*^^*^^ fG^v*^A.W k«3N*« Www. ^^-po^K>3esi b*^dfef 

3|3 ma^ fee |^wv*4 h>^ ^i£ vUu &{ §%^-ii^ heeaho 



§311 FLEX UR E. LONCL COLUMNS, 151 

3(1. MOMENT OF IHERTtA OF BDiLT COLUMN, 
EXAMPLE, 1% 15 I^To^o^ed +0 -|ov%w a colu>%i%i h^ ^o-iWoic^ 

-Hi^^e k>^e^vt*i* VwmaV b«. (slou;^ ,-{^5*k csuVe ^ c<?uciifNL c^^w^bg^ 
■tWi -VWe Ud^Ut^ -H) -^wf<^ €U«jU b« ec^u«l \w^C (XkI&I pWeifij 

I^ ($€€ F^. 310) tVs •w/avw^td' o^lv^f^ alb(?4^V rte web- 
cai*. fee |t>*<wM^ W\ ^k€ KfiiMjL-boek o^ tk^ hr^^i e4jw^«%^ , k^^ 

i^H^i. x^ ^ ^ 1^ J oiU >bfeii i^ - -2 L^i- FtB ; 

>=yiBp-£v 0) 

WcW UoiW+ X-^'e^w>^^Jil*"'n\>s. )t>^ Wee H.rSi^l 

ciM Xy^v^. Co*..^ «^1i^« \\mJ^ book \«rc i^ -Huxt \¥i \k\$ 
bcA.v'»v X^ ^ l85'.4 biqu4Xii.. iH<»W^ av^i ly ^<J»A3 W 



X 



yfr' 



^ 



y 



figs. 3a2, to 32 6 Tcface p. li>2 % ^ 843 r<, 3if 




lyjLiiliiiv 



l^ick"! :5r 1> - 



Ji I 






IXUS 










'■ "• ■* " ■■ " — " " • " ' > » 

As mt ADDIXIONAU EXAMPLE. , :su^)ao«€ Ht^ 
wo I-b^e^j/v*^ vwviitV^ b\^ )3l6:tet» VM.s^e«3ui 0^ lattice. Ld 

3/5. TRUSSED GIRDERS. WkfeH^akoux^ 

^!i3ci^ ) Taki^-fW Aa^« of uw^f;rm U>et<ii^n^ ,(t^i Ua<3t ;?W) 

'•^•e press tA^e |»ei-v>««j<2yv 4k£ po^v ouvui Hit<j b^a,wi H s P'^/^W 
>€(2. §^273) y^t^t bv^ 1iv^ ZI7 (?j -forces {5f€ -fuj. 3^)il^ 

r^civce \A/<^ are 4o <3oiAsl(ie< -Hi^ lv«Lif - b^au^ BO a^ <3l*'j^w»»- 
^^'^ /^6 "W-fo^^o^ ^ as well ci<5 (^^ \2or\itr\^ o'-\ dooh-thiA^^vi 

ivv d.fxA^ert)M^ s€^-VioK , 0^ (^t-tjv2 also §173 a^d Ft a. i 72) 



§313 FLEXURE. iON£.COLU[V-N$. 155 



Here I - IW^ te^i^rife.^ ^S » Fi^. 322, e - tke cU^ 

EXAMPLE. If Hv6 ^^ants 50 f f . ^ ^360 i^., tfc^ 
<^"tvde^ a J5^ iv-ck VieAvvj I-b€<x\u of wrouxjkf ir^n^ HOO^, 
H rke x^4l, tK wWdcU e^i^ of /^ - 7^ iKcUe^, F--2C> 
s.?aHv , d^Md k - 3 5^. 3 s^. ivu^kes (lais:cv. -^roHt -Hve T^wUi 
C^^s Kawwi-bookj, rebutted HW ^<L|e6xidl W, Hic sWt<r 

rr-k-rVAK. atioWAfol^? C^W^)3r«4$tOM. Sf^e^S, W^ Vv(5M»^e fryvv^ 6<^.(|) 

if. 3^650 lbs. besiiifis tive \«eii)ht of Hte beam. 



• [Let Mi^ ^HMiewct deSKq^\HieVie\0ds[akK(iHie^hriL:)y 
3/4^. BUCKLING. OF WEB-PLA'TtS IN BUILT 

tK(r< sfef\f \^u\k web Htxi^s ivi btUli- beawis ,^<^ccaas I 
b<2aMv« awv<St box-^^irders , /^-^uc^kt i4,e£(i ft) b^^K-^^^v^dbxj 
rtv^ti^u^ T lroM3 OH -Hie «'{<tes of tk^ wei^ . (Tfee ^/rt^fefs 
kere 3)ju;k;eM. of A<re korlxoKW owes ^t*^ al^ vvu<\h1~ b^ i^^ 
-^€1" e^wT^Us^ (X- rai.Wad<i- over O^skcrt -^l^ixrw o^ ^t, h^^OjeiA) 

cuM will vusw toe a|lv«M.. 

Ih Tii^. 35 3 w^ K(XV€ ;, free, ct ]^iH^ oj (j^loev^t P 

~}\ r: tk^ k,<2<<^{it o(-Hie^eb. Xv^ sack A beawA. uit<i<ir 

to^ ^ -two e^|:?ps^ s€cHcvte . Tkere b ^^xp^o^<^d'^b^ -iit 
Uoci o> -H/u^ ^riiOK o^ Hie b^^jti^^ , UeiuJC H^^ sk«a.rs at"Hi^ 
Iwc? c^s cure e<^u<il . Now iite^ ^k/e<wr ctdHwc) bo.Weei'V 

H*.^ webj i^^^^e i{ Vk<a web ato^ie^cf Fiq . 3Ji.3 ^ii5 sIiktwh 

to war ;p<i<:^<es. Each, of Hue-ac -- X ^I'ne^ wc l-uxi/c itsk««.a. 
Kcrix^THftxl 'IfeJvoqHi k -n keir^kt of Web. X^^ ^Hiis ^^r^^SiU^j 



^3h^ flexure:. LON& COLUMNS. 155 

AC ,, bv^ rrea-Hvc(^ csuS |r<e Hv€ ^irv^ AC of :SH»all wl(iHv~'b,. 
iirecHoK. cf ivs U-iL^tU AC o-tt Hce hxrrv.2-4>H^r^(H3i*«4«Hfcd*4is 

o^vwe. w<cb >>UH^3^ Via/ivu^ avaUjue o^ k^ ^/^l^^ ^"^-^^ 
g 30^ ) , aud wtH\, |iVeo( (ot fiart^ e»uis , K«>vw I4ve su^a of 
Hu^ b^rMUxutl (ufii^)pe\L£*KH of tk^iwo X'^'s at A 1:5 

zr-h jt^VJ , a/*/<^ -Hie ^KeoiJftY^ eWc«^ (tk W ka<5 a^\*t.^r^' 

o=-s7^ - "^ 

H»As ;^wvx , Wf H\. ^oct cw4/$ ^ would b« 
^ -i^tlo, 36000 ^fOOOhl, 

POUI^D -:A,wdl INCH-) . 

k.<vaAs ^^^^Aoi fo Hj^Cti*.* dLe(3tiv, cf web), aUw^ tiui+ (mj^-oI 
EXAMPLE. Fi<:i. ^Z6 , Witt ^rtftevtlvu^ ^ie^c'S b« t«<^^ 



1.3 ''-^_ EkrJ<URL.A.ON&C0LUM {VS. /6-6 

^. — 1^~ - ^'^'^^•'^ ' ~ c^) 

ISOO ^s/^y, 

HeKe sK^^ewi«^ |>t«ce^ will be u*C(i€<i H<ay-i^k£ <*«^fe,*- 
ihes cf -Hve <^iv(Ae» . Also, s-Ihcc Hve aU«u- ^ HUs fic»e o^ 

w.U b« He€«Uc( frrm. e^^K e^d w^ k <x dlUWee of 

CHAP.3ZIL. 

Linear Arckes (of Blockyvork). 
5/6. /^ 810CKW0RK ARCH, is a^imcWe^s^t- 

VVvP rcf^v^itwce +0 ^miiiit^^^iov^ of-iV3 'bl(^c4<s , or vousgiHTs , 
ii^ v^^o^t^i ()f vs/kich,si^.UA^stt^ or briok, ts kcV s^+^ 



% 3tS' LiN£A(2 ARCHES. 



57 




ory , Syrn m dry ^f -form c^c^i 

ear arch ^ wVuU veWv^^wy tKe saive $kaWs ^ ft^etir <^ej>Ik V 
To tVie "fxi^er 1£>«v«ld 0k5$ur«ied ■»= unUy iKat it tv%a.y nol a)»- 

pear inifr 8t.6 fermiAXae.. \K^ jo^^V^i Vtlwcen H>erv\ «y< "1 lb 

3l7. INVERTED CATfrNAftY.^<^i^^^£AR ^^^H 

■&\€ i^invl^ly Sivtd)1 vou^^oir^ t»Vva«€ w^eicjJ^i^ uMJcvrM^^^ 
d^^VtWii^ akwCf iHe CURVE^>Aye\t|Wvv>j a lbs. Wr >unm»i:f 
*.v\\Wiutw of 5u<k a. iCVutctuvie^ f^ . S2Sr\^ 




cuiuliV)^ 



cl»U<?nS ^\ eqUfclwY^CMn a.Y»: i^* 



^ Tl 



We«r\ CTn^^v*^ m^yexevH vou^vsoiyvS «dL a^y J>«r»^t '^^j'^f 
1he curve nuA.st V< TA\AQ<nt to me> curve », -^n^.:^ 



^ 3V 



LilM&Af? AHCHES 



S% 



wUUe ike U vefl^cal "fovcescict 
f|;ie a;!:U IXl. ttevic^ frie cht^^. 

wind 5^ €qw-aliOvt iS 








-'X 



^+c=~e 



e'^-i'.e 



J 



_ oa^ ^S ^fa|)<^fl«ln Ba^e . The Vai-a- 

b^^ 'pUttm<| X= OL 'Hne lici^f S^Joiv^ ,^«ct «/ = Is tlie "J^if, 
]K«n. ^oVtw:"( 'for C ''<3;y 5i^<;€$siv<: aJsj^+oXimaTvinS , Tki£ 
'VsoYaoyilc.( TKri^it^oY H^ , iS — cfO ^wKiU'if S •= W-itli, 

T 



•V 16 



WsH <;c<Iev%ay^ curve ^ witnTotvits "^ to TK(xt cut¥€ diM«f( of 



^tt Uc^ 



33! 



•q 3f 



LiUSAR AHCHtS. 



]j1 




3)%, LIN EAR ARCHES tu^aev GlVbN LOAD) ^aQ. 

^ PROeit ^A. Cjife<i tVie fovv^iff H-ie Imisav ayJi\i 
^-C'] .A iS >ei|uA^er}. ^^i*! li^'i^ Hie Taw cjf v/sprlicaJ d^|ilH of )oad^ 

f" t <2 , 3 3 2 ..^ >j ?v' e v\ ]h e c uv v e A S C 
l,e., me linear a^-rVi vlself jV^c^ati^Ciflt 

ike' {n»Trv tff t"K6 c^we HON cv 
^^XL 1ht )\K)ea\ arc\-\ ABC ^K«*<^^ bc' f^i. 

ateS 21 T?^VvAjeerv H-x^ two jmvv€$ tf^ ])rob«Yl?ona/ !o Vne 

load l^g^—h^ ^^^^'^ ^^^ ^^^ *^^'*^ • A^^a'rv«<^ ou lit^.UKt rt'l* U^:*;/ 
z at 1t\e, Crown ^oL l3lea':»iAye ;» lKewi ye:c^to<.vv«oi tKe z c'f^^nv 

'brobiem iw^^W lae solved n-tec^'vcwicaUj t>%,' ckW^i^m-cv^A^ \i»ii 
«re Kurv^' ortiev lifcavvj ccy4^ <5kW» 



Rj 333. 



wVie« 



m ecjr 



wvliort 



44ry» , J^^ v»Yy»«(Vi: 



^ 




kAC|lV>5 of rt-vc t^^^^ ,<!^vt4 tKe*^ ]poiVNi5 



o re ■ 



^-3ift 



HNi;\R hRCWf S 



00 



Ti«ci> 



•y .jom1s^^4icV. br€^^ eX^rUil^c:^ HiYusI: T ajam^t t^t'orl 







fn e<?»JuVibYiut>-i 



bv^ }],e 



<:*^^ liie /wo tH ru^ls "f 



'"" "^ "' sK<?ws Vke^mt A free. Fv-i?*^l'Chey~ 




I $n\ 5^ 






& 



TKat»f^*UfV 9 iS li-^e S<xn,e ^0, c^M \^^^ 

Voa^T .7,na h#nc(? ^, H^ the itnTUstc^t 

i>K. crown JvK^e Hu: ^^a f$ Ui,rti.o^t. 

ol (if anvj iHrre),, Nence 
.N^. a.^ a UW mfi 1 to T ana wr.te ECcr^Uns, ^ 

5i» 9 Sin a ' 

rni,e li. number qruJ H.<; lea.^ Cot^^^xu^uS . lack v«) Uc»«.- 
= as <ir. e1e.-..l 4 tKe ^„.«v «vcH . /? ,5 tk* «m\e Mv,*« 
Rvc c..,.c.lw. as s , e ,. IKe <x^^e W.een lU ^«,^,r 

is'i . TU IS Fw, 336, vf ;. ^ wewkt ,ff a 1 W 
«{ tt.. \.«a.. J , P = ^ e ax (• Tl{e lan..W <^ «^V o^^ 






t) =G m, 



%9l8 



kJNfcAK A^'CMES . 



Ifiv^eer. two conseculwe Un^eKl 5 r, j 
cuY^raWf) Henct £<!■.(«) Wcc,,^ > 



^^ax. J: 



ds 



/ 



Z = V 






' ^ 






m 










(^) 



Call tke >Wiu3 dj Ci^vvatuYe at l^e 

a p.m. .-f the Imear avcVv wKev. IKe W?..n{„. ,s v«v- 

fov m^fence ciu^d not i=. us.d as aU«e«^ c»rt% 
Sll ClRCiJlAR ARC AS ^(MBAR ARCV(. As- 

.^ let us a|>^.ly e^, (i^) t, ^ ,i^^,^^ 

•:">C ^'^ ' 'f'?- ^3 7, *» a !;„*«> av.1, 
^>^ Sirxce for <x cWle p .^ cor.sUhl«...ii 

^= ^^ ^^-^ 

^ Sin's 

Tlie linear avck) v.'MVi 1lie verVeal. ' ' 




%3.H LfNg AR Ancn^S }6 2 

Te {^ iW ae{>^k X % CONSTRUCTION^, l^avii^ • 

**' ^ -Z wfS ^5 I.e. ^z:: ^ . ^.e/P, 

3^4). fARABOXA AS jUNcAR A«eH . roa)^-^ e^. 

^ ^^* ^ J ^ Jhe*-f»^s -(e* a>. j^ 

o^^^ 5^<»h4 4^^erp*>tai ee-€Mt^cv^r»fe ^ihwiMe^Vo*ti tH<. «ttut-. 



/■= 






At rt*e v«t«, e ^ to' ^'" ® 



5 3510 



UJ^^Ap APXHtS 



16Z 



:^-2^ =: CONST A?^ 4f4^?3fl (7,) 

izdrui^ . TV^*^ re"=?4-L)t ■mt^kl W\re V«cn 
^.^ untTCr»w4^ 4f*ir^i>aW Wr»:2.£*^Ictlly . 

321. UmtAR ARCH. FOK AGv^t?^ c/F?£K tONrooR 
of )j2APW$^tVi€ arcVvllidf Wm^ IKe unknGwH\ff\/Jc am- 

W\U W in ex^M^tbrnirvt uyu3.ev tKe loai/Wv^eevi ^fs-elf avui th^t 




1*^ 



^ 15 Qjv^Ti ©r CJt'&suJ'^re^:! . Z 




il^ru^ ti** art. JVj^ Te^^<im€: OT'^y^^ 
c\ iht W>-t^r^es WAf avJi BAC 

A* Wf«ae J rtit l>auRin^ jS 1aomcx:^-enet%r5 So that i?wy ^httWhs 
Curves. C ^-^>^2^ tfrwrVnesS 1 To )j>o^cr^ Mcv- y^\Q . 3^1 




J 



Imeav arrh a*^> Two \ti^ks ^r Cowstc- 
cvuve blociO& 1:>€ar\m^ at %t\y juv^c- 

s-tijW- of A. cui>ic urnt of t^e lt0id' 
I| T ou^t^ *X^ 0(tt. %t hr^^h 






■1:1 



'%3^\ HfiEAR Af7CHeS 16^ 



€X«"rfe4 on Utft^e twvj 'oi0^<y 'hy Then* n^t^'^orsQ^^''^ u«^^vStd 
y^xrrt^'si} vtfss Koivf: iKc "Iki^ec f^c^ ^^,T ^^^^^ "^'^ 4orMm^ 

:SY= '^^ T'sm^'- Ts^^f = dT ' (2 ) 

fr<frr» {l)it o^^e£r^-*i thai Tix^s^ ^ cctnsWt at oil bo Wi df 

Sulo^sWoAliJn'J -from k3j m (^3 *^^ oktavri 

But Wi- 3*^ \^ 1a^4>*^ i£ii£ ^ C<^^ o>..^!i^() 
v^/Vilk dF= K(x*-f :2*^3(lx. "Het/Kie^JiuS^ -jcrr rtrnveniev^ft 

1oa^iui^^w>ioS« tKoitH^sj - unity aA;t/ wk«s« wei^^i ;♦ Hj 
w.We Jiil^ J^r^^^/) .• ... (5) 

iS to be- Vn er{U4Vib%»um under ttwi lead (acW^^d ^-efweev^ U- 
6€H o>*4 tl^e ^«v€W ciAVve wKoSf? ordma]>$ are -z'^f^^V SV<>* 

32?., EXAMPLE CF PRtCHt))MQ. UPfER COHVovfl 
A STRAIGHT LIME. F15. 341^. LA Ike v^^er <wxSja> U 

*^ <ff t4? . 4' Wtw»kr5 2 <^ vo at <s}i 

'[MH'nis df ON . Hence ^\» ^C ]>^rr.t 



iHS 






% 3^2 HMEAR AF<C'rlES ' 6;S- 

we ci^Ta^'n .^' Z ^ r _ A, z<32 ■. v , .. C^ J 

Vh.i Wm^ IV^-e of iH& z,<Jz^ aV ^^-^ <ix 4ea<^ e,'- 

•bomt w av,a ^»»t "rtie WW sj i:'He "teft-Vaarwi tnwWr* of 

- A . '^fel (7.) 






diZ^a %x^. 






X\us curve \s coW^ iKe T:^AKSfOpMf BaT^W^^-V 
a. w-ere =^ ^ tKe curve wocaW Ve a comrr^ot^ <;<aJfcio«ury. 

%VK TKe curve <jr Imeciy arch, ^ r>om £ij. (^^ v^e Wave 



^ -j^r^. 



LlNtAfi A8cH£S 



166 



orta 
t 

00 mn 
'1 



f,«>«S 






X 









1^ ^ 



a. 



(to) 



C^ll VW arexii^A^ Af5 fey rt>e ftrr**-^s ««t %t 
ii|{crent j«v?^S <!r{ tite "Uw^^cscr orA ., See Ft^?, "^"f 3^w« iu:o/^ 

•L&i :A, H.I 

— ^ r-T^t * I \ ^^jj^ ^i any j< 



0' 



^- 






% 



^*^'*^''^ _35S. KtMA^^KS.Tk.jo,.- 

q^mC' TreSuUs tvva;y be uti^irei \M\\h arcKes C^ ^\n\\t div^fn* 

ttonS of -fricrvon and iKe re^i^W^^S cj tUe marer^al 45^ ftif. 

v^»u.SiM>rrs ore T^e&erved ^or a ^(^ficteaiyx^ ctva|>ter^ in vvHUk 
v*^ll W a^vRnr(?ri ex more jyratTlio] iKwsry <i<:a\vny W^rti at- 

^nrtjytwol'e linear a^eVies cr eoiiiUbnuin |><jWy<?ws a.s t)>ey 

vviU then W colled, S\A1 a sWw o| 6:^a«[ linear arA^s 
\*i v^uuaiale on mcmv otccx>ur\fs . "&^ Wertii'-i^^ l^e \if>Aay<:rrcKt5 
St 'far y r g& a- ^W d v^e- Hove Hie ^imrs a^^sumea V)>^ [lejt^Ue <\wi 
ik\»^l^v?5M>\e cords, Iccudeci m lKe s^jmc *^<^V » 

CH/\?TI!I, £UeT.ls4§RApKlCAL5TATrC5 

3^^. DEflNiriOK', ^rK many re^^j^eTs ^r^Wol yn^t^ 
6*3 VuAve aiJvanTa^es <?vcir tVie ^uye\N aruad^jllcal . wWitix re* 
Ccrr men i lUtir »^^^ '^ r>v<\trvy ^sWbletvis w;KeY« cel^r^tY ts 
At^re^ v/irticut refvned cMZcuvocy. One o| lV»ese <a4^an* 
1fti>eS \6 \WaL cpTpi^ errors are t^ove ecii.iV*f dererfedyCivKi 



i^ 



■>).red.creri tit .:2.QWrce. 

Glw;iitnAL STATICS. feH,e s^n. 4 a^^^^ 

q Cc^ic res«Ui^sk^j4 W mlevl>reled k ft,& same s<«le 

!5 ih€ U^,s tff all cc»^rud,on^ fr MmWnms and res<,}v- 
\n(y jsrces. 

336; Fci?cH pciY^OKS ^^ COHCVKUm fom^ 

^ee fisrces T P^ <^ P^ C**^ IWe same ^a«^ ef ^m^^c) 
R^^.a^^^anjr cue of Ihow ^as P, ^ tnast W e<H^) and ot- 

/! / 3 off to Sotvte col^vev^U>^t sccJe aVne m ^^q^Z^$' 
p^Y ^^ re|:>r£6ent T c,^ ll to ^ m Fi^. -3*^? 

-p ^ mKst "be ^c^Md il to :r^ , srvice tkaC V«n% 

_^'^ -^c OOSe Ike hr\cK^k •|>roi,€rl/ Ike d^ecticv-iS 0/ 



%32b ^i JL^„„^1^^^^^ ii?-- 

Youfui the i^^inj^Ke.y, Pi^- 34^6 j, coaWd oi FO^Ci: Poi^- 

^ON 1 c-j ih^et si<ie^ arAj m Ums ca5€. ^_y means i)[ »t., w-r 
<^n^. ^^o cf u^e ^t-iec ■]<>rceS wK^ V,ol3 tUc 'hcmt \n eoiuliha 
uni ii-^e tkiVa CAn W "fcvATv^ btwQ t<lu^ on^ \\ ic llji^ *»«3c 
rcC-^SOTv^ 1o close* iKe •forc(t bo'^y^en. 

^H-lj inttst clcsej wVuilevev Ve iKe order m vJWK ^U SH^e-s are 



p 









"^ %3^6 ' f^^j 3^'y point O. If P ^e.j.^ 

16 t1l€ yjxkucNAJn force wV%fXi is Ig boW^^ tfcc ellier ^c«r (^t*€„ 
sS iK<tr an1% > e^a^>^a^n t" L w c draw jKe Sides oj itie jertt >«iy 
4^c.n {rofvi A roK^nei \b 3 ? iV^n tKe line BA v-€J:>iftse5'jU ft^ 
r<?^ta>tc! P m oriMJunt and iir€<i*n ,*»h<:C IWe anoi^^ B/\tt»4»st 
{olU%^ tire cs»r«CintA4(y «f Uie #rt^evs ^ ^4«l fc Wti} F«"^^ 3^f7 

J-f iKe ayrow BA w«ve Winted at ^e exlret>iiy "B^ IKch. U: 
c:;ive':> cbvicoAsly , Hie atnaunl and dvrcAon </ ike xeSct.il:ir>i. <ff 

Tern 4 CONCURg^^NT FORCES IK A pLAME fS m etjuatW. 

32.6. K^M^ CONCURRENT FORCES i^KpLAj^f. G^i^k 
a 5;^ Stem df nai«-<c*\cucyr«Kt -{brcts W\a. \>Unc, ocH*^ en c;?."n<M"<i 

at«4 «^rn.i'H resuUont ; cU^o c| €x|>"»'CSSm5 conattiljns <r[ e- 

di^^«Ucvi' i^*\<d also m ^55jl*i>n C^-^* ^"^ l»we ^ curfion muit be 

^AekYmw^al). E-g",i F*5, 3^& ^rv^A;'i a curveci rvftd Warn fix«fl( ?>t 

i. V t5€ at T, anc' aIsc unde v tKe orion of {«.*rtc6 |^ P^ P^ a<v\ 



^'^5<i <^KAPHiCA.. SinT'f 




S^ Hit r>v\ii -+^ 

Wn<^^ <x^ <U/ain <Jmwr> W ft^", 3^?. A/fiw Since ^ ^ 

*. -«-» , • c ^ 

<»^Tinft in Sk ine 

. 15 

'f 








\ / C...F 3--S 



r^.... i\ .a ^i^vUv 



(C) ^*K*t a 'for<r f?^ 



"Wi ^K »t« oppcs\r£ a»v^c^tVn w#uii )>4«»^4K f ^.. "P^ . 



♦rtw 



TH*l i^>c V<^ P, ^l P^ ^4 ^^ ^^ ^^^ f 

(jj li^> ^a*<JL iy%akai^ <^^ -<>Wr i<>^^^-^^ Hi^i^^«^-- 



% 33(> QRAPhicAL Statics 



170 



"KftT v^rt!^ ^i|. 5*?0» 








[<?<e«r ]f?e)<^«^<}*i (Qia^Mc^) ^^^ msc. Mejfl nete iVjat ov: ^ 

i! !© 0<»% ^«4i wit C'V; Vnfe If Iftf fctff <^«ijt« 

>i4s W'rt* ^iwim (tiveW!»»iij S%€ KAY$ as lUty ore ^^^^Qv. 

1^ alun€ fife 8 t« 0« 1i W#**€H t^ oi ^Ofme Jwami^'b^ 
ftp If t<, Cc* W^^ Wc 1W r^^«*Wei W o{ 4r1»en ©t R* 

Oft^ Vtk'h Wt fwo 5<^>T^gvlU olo <XV\6 ^ ( 4t*iK1Wc i»*»€v 



<J 



ClJRf^£KT FORCtS iw a Vione Nl is nc/ces5ary -n^l only 
llaat ifs lOYce i^f^^^££J2 n-i^^^t clcsg ^ buC aisc fhai. tWc f-^t 

-:4tail c<}> ]nctd<^ vA^tm trie re^iJ^Tanls of ]ht -first Two -jorc^S aw) 
0^ ftt V^ Iwo jor^s t^c^^cWely cj{ tKe* System. E.^, 
al-. c6- ^>^cV^€i v/vAnx tVie line tf{ out ion of ti^c rtsulVbhot of 

c{ -f.wces ni 'tVie -{ofce ]^<5Uat3n ^ or dlvffer^nl ckone tjf a X-^Lh 
O, 'Bui if me or<^ev c4 forces Wjokcn a^ ctbove , £vs Ihcy . 
;>CCUY aWx:] flit Warn or 'sfruxturf. ^ cirui me ]xie lakevi ^i. fte 
j>ail''of the flT^t for-ce in» tioe (orce ^^^oVy^oi^ , "Vhcve VAF,U lecrt- 
\^cpC5 (^a^ !kv5 one wtU U c^^ tke SPECIAL 9Ml- 

'Vru^ ImeAr arcl^" ilc 6ea}vtiG ^''^^ ^ stone a^H . Aflci- IJi^ 
PvAYS Tc^tlfid m hi. 36 [^ Kave Ween (xdji^d., y>y ^]^c^rni^D i]nt 
boi^ to e«xk vertex vA/xHa. wKci^ it u rwt ^auvcajy conj^^cled 
rKc jii-^i f<^ure Tvvxy V«- ca)Ucl \W. fire^. 3ik ^rW - 

It YTK^j i>on^li*n^ V<i c<mA^Kie»»t to ^we ie viA«vwi «] '^^ 

in v/K«'ck Co^e rt\e •ffrsi ari3 V4^ se^^wevits <5f tW<^yrre^|3o^ 

Hx^se forces \^ ^£^ B-PACP- D)^GRAK Qas we ^n^ c^^l 

^rc:e< aii» TViiS^'^soxd Auj^prrrvi sVtows Ihe real fveU^cuC. 
Wn ifj Irit -forces J wWJle JV^ (o'rc(^'Ala;J^rctT^ _,wKtcW vwca^ We 
%\acec m civiy cov^v-evii'ewi |)o*^Lon 6v\ tne 'W>er ^ sinews llie 

ev duau:'>am , its \\nes Wivu^ tr{lfiy^>reitfd o4^ a ^»CC^ d( sot*<a.ny 
.Lr=. oyIoviS "to tlie inrk <5| kai>ev«\»ri. the s)3«x<.rdU3»a^-vt;<iai v»ye 
ci-tJit wirti a- S<rald ^ S<:i Vv.^.v..y f eet to t\u. \ncVi C^ halter 



^n^ 



QHh?K, STATICS 



17^ 



cat^e. i» now MK-en \* 

. ^ .-1 X/Vi^ 



closadl -jwCjC ^oU/<jo«. tc toicn as a V*^^^ ^"^ 'ray 6 4irA»«^*i |rom 

ei^\%pc4^^ia art«wv\ m tWc s^?i*Cc diagram iKc -fi^sLani lost 

tf?^ loM. "^ov<€^ q^LCcr<iiW<s to m£ ord^v aJUj^fctd. (^or wtrii }f\e 
TteWlWtts «{ {Ke first two orni Wt Iwo ^ (f m<>v< Co>»ve><i£H£ 

WAVL . Tnt ^va|>K4C relation^ jtxst {otjLrx^ tnoy \?e tMoJ^ 
"fee TYveatvS rf 5<Hvv«)ff WoVlcmS mvo\vmy n^«-(^vicuTry^nt j»)^- 
tc*> m a )fk&rte ^ ^\\^m tWcre or* ivia%t tnree uj^kkowh ^aan- 
tvU'c^. A ca^e l> n(?w taken l«r *ijWiiraUi« , fiV 35 X sV»ow5 

a vo^ Viin^edl «t O Wn- 

yerric^aj wall oX ~3 ^ 
Hxe f K&r 1 jontc^ ) fit • 

Force. iiflu^wkfn urc at ^ W^, 

<iir&eli<5n arv^ Wvvtc reJJixc^d ^ its co^M^^^ejats \(\ "kMA^wrudi* 
yecWvs. "V^ fr&L su]>^05e t\6 l^raVUm t^lvti, cfradikkal' 
\u j^ ^^ to U^-^i^ of tt>e Wsst mettuKi o\ dteRnrnvw'vv* \Sfc tiw.* 

"hWs -in ^f*e dtxcjnr«xmj ccmStsfe <^ U^^es Wd 4{| €V\3. to 
«rfccl , «i»*d respectively t.o^J^ omA H (I^ scale ^ ^ H^e ^orcci 




^OIA J i i i4cp ram 



PH: 



% 3^7 <;r apk. statics ijs 

foTce V 3 «ivd tKc arrows tno^t )iaMe a c^^tTinu^us scnks 
^mt \c ^ Wn^«r«*m^ U»€ i>o\^y«o. For Wni elosni^ ti t«iLt 

and ct>^^ in AiVecTt^n * olw) T^ v iS e<ji4al »«« uirw^^^ui^r 
tc S, + S<^ ,<»**d. «^^*;te fey tkafn w« ^r€cL<>n^ fCorre^* 

Kc?i* Connect Q^ ^as a. *^€ , witit oAl 1^6 Yeyt*icS jdff jfcl 

^ «on^^r*<i 9A raj 6, AW 4»^«»/ |^*m<D i», fto. s^c- 

dw<^Y«i»« ^ ^t lvr>€ Co, B t« ^t yoy ... t \n ^yt ^Gr4t 

OL ,<ivAW a \me. jO^ t to ike saor^ raV 0^^. % ef 

'ijttJt IKe ^ccovi^ -my Vuoei Wh dipown » THt^ ^ecoK4 S€<i- 
tv>evit flr^ tWe t^^tul, ')pM)'\^(3op skaul<i %Mie t _, J^c mfevsee* 
Iwn d| Q iWI If in rfekt S^jiK*^ (Jii^-rftm (^ 'i^ Y\ot ^itc 

*n^e lev^^rti (j{ %t ^trst vo,^ 0^ •,. I gives m« OithW 
(?{ tke -resutfbint 4 ^ *'*^ H , ^^U Od i»t tW sJmic^ 
dlcujra.1^ is ftic \m€ at c^cn «t 1^^ resuitarvt, TV»elf4ii,yft 
«|ll& S€toni YO^ O^ •.. A tJ^tvdS IWc ^m(S4wt 4 ft^e. >c- 

Su\Wi <s^ ^ ^^ •^ ^1 J"^ '^^ ^^ <^^ %t s<£* 
ov^a ]*in4t<5 re Siiltan^ avu| ha.s <xe ^y fc lilvf ^ ac- 
tion; Oiv^ 5a an -for rvtave^Xe^. TU Wt ^ttw^ >€- 

vey*H?iVvim^ -forces • Iri fri»i Wv«I<uue •. * S. ^ ^^ '*'^* 



§3g^ qRAPH lcAk STATiCS . • \l^ r 

^uJWi ef V H and G i^Ts aicn^ aC And tol^nftS 
V.-e ree-ulWt 6^^ H'' awd G^ ciclin*^' at c ; or, if v^e 

rorv-S liier U .». 3 as « rav iwe >v«aw Sa^^ ^^cA «.r 3 (j3<m?t- 
lr\i> tcwav^ tVie Ti-V»t^ i^e TcSuilar-t of V H t? A»aJ G., 

<xcU jQionc c?i5 o.r\^ ixxVAOces H .^ o.*^^ tUeK wf vyoulA con- 
sA^Y C^ cu^ Ike last se^»nent cf me et^cul ."jxAy^on. 

It tS ev'ident ^then tlial the se^rnei^ts <5f tie e^uW Wv[- 
q^a are tVse liaes d( ocTion (?( {lie 5<.'^xess^*^/e "I^ArTia/ resu) tW5^ 
viWj5£ wuiQniWieS vviu,s1- be lo.k'^n |ro<-v\ "the ccv»^«S^hJ(.k^ 
Ixxvalle] Yc^yS o"f Hie ^orc^ ctiAyvam . 

v^e >ii)w proceed U/ "fiVxci cut \\o\m {nt unkv^^:n^/^v l^arss tnexy 
be conslrucVed -[rom ftie H»aowa^ trie WHev- Wm^ (J^ onxd G 

ihr Two 3icl€S (^ avv<^ Qi^ <^%t -force |x5)j|^n ui It^e fo^rre 

ul %t \\r\e.'^ of H ^i^ H . How skrJ) t^;e c^elerrvMJne O ^ 

5 he pote *: 

5ult df Cerr^l^mirw H" wilit ^e. reSulWuC ^ ^ and H w>i' 
b€ a -jorc€ 'ba.5»5inO' inTOu^i m<i point c:^ o^xk^ c^tm^sI aw;^ 

tke reSulTant cff Q, oru^ Q^. "'^'-'^'^ inTeysect H ot OC an^ inw^ 
leifymirre c?0 "tV>e dtv^Jtcn 0*^ a ^ne ^rrst Sa^ment o[ 

G^ cin3 S^^ 1^ n/.£)st c<7n>^eyv»er)Uy faancl loy Hxe >iext j^am - 
CjrOL^k (32 8)^a/ui ttie Uii^ <ff action of H' vS krwJwH^ H^'^^t 
<i U derermined ],%j iView inlevsecKo»7 . TKen l^^ dr^w/t^.-.^ 

wm%6K \s the u-AV^-ysecliov-. of )»... V vAiti 3... n. "^',lii 



%SQ8 



SRAPK. STATICS 



lb- 



coriAe K>«iiJMn ^o-na.j>K'<cally ajid s-VM^^kV be scolct^ off <xct^ roU*^^ 
its U-vt "[cnrce - scale. c^c^Fed j "^*^ tke ;|crce diagram , 

3S<\ To piMC THE 8ESUI.rA>/T OF SEVER- 

a} lei or ne^i-rly so^^ q. 6^>ecla3 Trt-etntxi w^ nov\j1>e ijl-xeii^df 
iireat coTvevxtenc^ tn ^^ucK cases. n<^, 4o 3, /^ec j r^ 



»4 



•jorces 
wKc5€ re- 




Q Sp«JC€~ ^li^am 



Rcj.353. 



anu^- re^uliqM ^or foTCf wVlcU wv^l VoWkce Theha^ ^ KU ^nV 



?-nfs X and i One of wVncn S^iy X ^ ^^^ flirts irorv m ^* 

i^ Te^uJve(^ fo 'find "^ . \ ne fwe 'fovCtS nicest "kn-wtr'^^ a, 
boLru^ced ^v stem chance }j V>ecjtvAnu\i3 dt O wt lo^v^-falme 

0, A = P \^^ scale J rtat A 1 = T, , ^-^^ 'io on (; |>o;^t to Lutt3^ 

H>e lire 'SO^ v^efe^1►^TJ; To close Hie -[ovce. |3o1>;Qon i^ c ^ 'rC- 



% 3Ua G^AP'H.> STATICS ^ {76 

('v.^Kid-; c=;nt^ec\s lKe |?cle 0^ wilk Ike ^ - ^ "^^^ ^^^t -jcvce 
\ngvitu:nec{J^ ^rom T>^wncy€ ai mtcvsects the Knt' of "1^^ ^ 
ar.xy.; l^C ^ [I to tUe mM <^j s^ 2 , till U inTeYseclTs tUe Tine 
05X3 ♦ Q^ lioe mc fllv^wn IkrcoL^K C ^^uacl \\ tc ike "f^ 

P TJ^ awd P ^ /, o? ^Ike mtevsccTicn (sf t^G. Imes <?f V 
c^^T^ M a pomt in Rie line o^ octtcn j| Hie i^nt"t^vesu.ilav?t vt* 

line- BA in "VKe -force dio^ain ♦ ^c?t "8 A fcnrrvi^ «3t closed 

liae IKvouaK c? 11 i"o 3 A ^ viz.. c:?6^ \s %t Ime cf-cfi^ 

of 1Ue anU- resuAWi (^M li^iAct cf Vhe resu3Vaw(j of ^ ^ "^a* 
Ptnce in ftiiS corvjruction x i^ a>^%tVa>^ we may first 

a, IjoSiFion ftuit ^^^ in^|?cclio!', tKc i^earwcMts erf tHe re^u-ltm^ e- 

^cmL Va^v^on sWl ^ivt fair i[hte>r5fcltonS and not "ba^ cfj 
Hie^A^ct". Xf tUe Otw^w forced are ^ralUl the (device 

TKe resu'lf (5f iKiS cowilr<xc\ion tnoi\| "Ve staled as fo^\ow^^ 

■xswdX as a^b ar^^ Iq): IF AlwY TWO SEGM^MTS OF 
AM taOlK. P0kYG0M,8E PROLONGED >€4r inTevsecWn ,s 
a \.o;nt t\ rt\e lm£ of acT.ou of tU RESUlTAMT OF TH0S£ 
f^ORCE^ ocliwtj at ttie verTicfis m\£y\/ tv\\vxQ Wtwetw. tV»e <?U'eH 
Se'^menls. Hcve^ tKe >eiu,T^vai <^ ^ ^j T' acts IKrou^h c(, 

3^1. TERTlCALRFA^CTlCMS op pibRS^^Tc. r.j 

35^, (qw€n rh-^ veytical fovces or locui s ^ "P <3^*^ T-, 
Ye«cli«»KS must ^e vertical^, v^^ccivei Hie rejuctiova«i "V^ <a^ 

"V flf tl-^e. |?ICYS. for c^K iW^Qwt SiAJ>|>0Se V cvvu^l V 



f339_ G f?APM.STATI C S_.__ 

"krujvn ■, >^e<j art m efuu. w'lrti p^ p^^^ ovJ V^ 



17-? 



T^, 



7^ 







c^iajjToni 



3> 



'v,. 



i''^ 



wl^eyfi tke forces vAm^ tcoA^ \ie ^ fee sat>i« Vnfi ^urt sJwjNtly 
>ej?<4r«le(i3 . "^Itk O ^ ike WU ^^f T - *^S a ^Oe drow^ \]ht 
rrt^vs erf ^e -force dtU^yann OA^ ^&> Ei4f The coTre>j>«na iVi^ 

Y . T<?\n ^71. Nov,/ Smcd l^iH4 "P' Act fa Hies<»fv^ 






iN4 r 

. nc -J COV nviAst "be IKot Tm€ ^sWi mui ewe \\ % V c^df' 

p civ»d P* ore arbjlTAYy tke l^^iitian (?( ^e We ^"^ «rt5* 
Irattf jwKilc P ^P -) ^"^^ ^ ^*^ ^^ ^^V r*^^^ 1<nownm 

Tak£ c\nM cov>vevvl£v\t Wie O. 3raw tKe vaw s OA 06,0C 
avr2\ 01), Tnen \>^Knm'>^<j at ai«.y <loiaueHiey\t ^ml <L '«n,»f»< 

1?C Vl ^o OB aw^ So on^u-vntd fte la<t Sexijmeyvt f dll in 
'^KtS ca5^ ) Cuts flie veYtic«:l Conrammy W^t uv'\Uv^ewn'\^ 



§32 



qRAPM. STATiCS 



76 



^, ^^!*e ^vr^ n . Join an OVj« is ?omer.Tv,ts Ca)lei A 
{<s.ce-aiayT.xm.~'rhft Wt !«,£ uiQ cof, a>e"')oaa-'lir.e " in 

v,UROkLAS<Y- &*;d«5,tly foi- a,<:^we«. Sjsl^ ,3^ loads, 

OF- THE- CHOICE Of a PQJ.£. 

-r»'^a bodv| c<3v,tern«d oore'^eft out- ^ atitwjit^as Wy 

TO A ROOF -n?U$^, Fn^. 35:5 -\W 






o/;-/. 





ttn,j J^^^^ 



■f 



M^ ana W^ /av-e 
1^ ^Hii IP aire 

ol fortes aye (he 



§S3o GRAPM. STAT IC S ________J2l 

^v^{^Vies all B>€ 'boVz^y*^^^ 7«i.^i<>lA*i^6 '^rievie «i Hie )e'(t'^ 
t a.3 off %c f>Tc€5 C^rwv.n) 'W^ W^ P 0uuu5 ?^ ik !K£ 

Tc c\ose tKc )>*^^M^^v« U is evjidewt we ne^d o**^ 4r<a.w o^ 

X , TVvcS cUleYi*uvrC5 H "^y^ v- rei«KA,\vt5 fo fl^^lerw^ihg 71 
Hie ^j>dmt «?( dinsiovL Wtw^en ^ et*t4V^ . StAect a. c4>H¥Gf%' 

?ent "^le O, J, OKnd ^ra.>AJ nri^ys {voiM Jt to i^S^lfc. 

1. «. »x W - '^ " C * " Ik-w** C *' *' O 3 " *' 
? otA^a T ^ (xvc U rtxe same Im^; tKeu e^f U to O 5' 

wi dvaw a U u> iC 

on. 
o^re vxow d^irrwneci as vueU <*-^ H . 

H^v^^ novv oill rtiC exQvKual -[oKes acTiHj tii^ttift Vvu,^ 

uol 'pieces _j o*\ iKe |(5]lcwin(^ ]>laii. TKe tVu.s5 t€i»vo Toin^ 
conyiecfed ^ t^y ]>«ec6 cytfen^iVij Ijev^oK^ ql joint cua<A <3xiVlo^ 
AiCi^r o>vtSwicycdL lb act</jcmB^ ^e, ochevt buJI\ ov ItS^tst, 
a{ Ci\cVv )>iec^ Oil iKd joint cA evtt^ty txrvevHi'l^ wiU W 



K'ow jcm <jt<7 ^ t\^e ^yos#vW'/jh^', ex* 



% 351 



G«APM. STATtfTS 



lao 



^ * j( ;> # *"■■■'-'■' ■ ■»-■■■■ ■ ■■..« ' » « 

i3t?^4 the. ^n. «rf e-o^V j«int rs m eijuAl*Wiu*n tattJ^r a. S^*" 

Tern ^ Ctm caTTty^t |owe^ c^an^^^ruy of lie 1^3>«i^u( <»W) 

]j!r€€«5 m-eeTmj ^wrrt , 1W€« w€ may <'^^ Mt bvwiajylfcS <rf § 
"i^S to <:U5|[Jv jm^ tn Wi-?, See Kr 3^6 




In Irie *!►<*« a'w3upcim a. ca^'itaX leffer [A 6 C tb»1 ik ca^ck 
tW fcrce "W^ ^ Ike -tree 'BC ^ <yf W «<. ftie |ar€< C^^ 

Thai (V^mC slVess ^ o^*^ ohjl|>^«^<? cavj Vc nam^sdl ^V<»«^ ffcx 
Vlli^5 tW l^£ Sj>axes bordCv^Vv^ ti:S lu-o sieves, Cfrrt?^4p^Hii«w 



% 33i QRAPH. STATICS /SI 

To ll^eSe CAJjtW IfitTers m ^o sbacgi <if liic sj?acc-i*c*4jn*^. 
^C ^ the force ^^^*v b«l^*^**^ fe Any Ji»^ ivi, v»^k^^U 

€i;^uu.UWA*.wm uncicY tWe eartrmixl wx:ev^ To ftn«i ttve "WJlsdf 

^ t^oi >{ oK Vat two tf{ iWc Screes dl cu clcs^ {ofi-cc poly- 
cksvv ore l<H£>wn |W tvrouijfniJixie 4>w^ dltVmion J wV»t)e Ihe 4iVe^. 
Tu^& onJy^ef ^kJS^5 two <*rt kiM^wfti ^ tke wUolfc ^cc ^ely<}eK H^<y 
^fc <iTra»/n ^1W^ ^ttErnvw.M»^ {h^ awA-ot^t s tsf tkoSfi Two jwarS 

^»KX«5 -m^et^csis at oC ^Jcall tTi£ j^^irits << p V S o^-*^ 

k»4*s^>M -force 3C (^^, W ^ l^omfinj %tS at tKc Uv^ercH^i, 
Tc «\ose iKe )>fli^ifon <3->-avJ Tlrrou^K C a II to ttit ^ete 

l?e ^>owt to tun trcun^ \1Se )>«vt^Vitvy , frc farce Willi v«K^k Ihe 
"^ece Co ocTs cwA the ^n d\ fee joinl iC ii a. fovce of avc 

cuiviitt cf tt\e )>«€ce J)A t^n tt>e )Hn <*t oc t^ ^rom ^ 1c- 

>^»^vd CC C**^^*'**^ <K <^Yrow) Ovtdi Wvire "DA )S W ^- 



§ 33^ CRAPK. . VIATIC 5 I fti 



ei m CdK^enW la Cuvn iKc s^xKi^i- ABC awi Dj,ir044«<) 

the j«^««t OC^ Q -S^UHtW Orx^er wtU Ve -foCkM^i cowYCHrem iH 

i?B l!?<^ Iwa <j^ tW: {ort:^ ocCiHj C5t\ tke )Hn ^t )W j<nvit p ortf. 
t<M^>i«an <v^ <?-«U:?viatm^ly we \>-e^t>v a ^^c^rce '^^^^oix^ p^j for 
it^^l jom^ "by ^Jtov^wo ac rr o^ I\ is iVe c?c cf j^&V 
l-jart ^''^ ir^^f ']x>t7ded in Ae o^/>o^e d2irclwn^u^^ 

1k€ acT^ei^ of CD en ifvt ^oint ^ \* tf^juuj okJI a^jxrWft fc> 

(v^-^ y an<A )>omtiKa fee -Same w^^ j Ui^w. 6f = <?^^^ U to 
I irAW a l) to IKe 'jK^ce F <5 a.W tWrcsUijk (£ a II tfl life 

OO 't^ m tension , o>^ 

Next ^o^ Ic IKe jVnt , a*A<i cot^^Kuct tt\£ Jxily^en {i ^ 

thwA <^<] CYmmivujf IVve st>-e^ otl im. C^H 0*^-4. tViAt a.a su 

AVt iVviis lost -^crt^C ai <»V^>a3<{ cVkcV wtlk »b e-j^-.^^ 

al^ ^ vyVos€ Vides are nt^-v kvurwn. 

tioS'incj "SiC '\><ii^ci9v\S o^-rtad^ ^vuL \fu 5ucW «. w^y as to rviake 

fe not So reoiiAj |>ert:eWed- Kevc o.^ wVxew IPitv co^kijat Sejsawiiie 



^331 



GRAPH , STATICS 



ft3 



9 ^^{ QvKAPH . bTAT IC5 Its 3 ] 

aWmenB at hc\\\ ends an^ not -^vcc U s\\6s lotcraUy ccl»41 

dw^clwii txol oni^ Cfc^ti the e^juAliiirS 
<^ 5tauas ,W. •n (Ue -form ^i<( ^ 
elasKcity e( Ike A^cV^^IVtcSS . Suxlt 

53X.THE SP^lAL Eauik.PokYQoN. iTS Re 
iATlOM To TK£ STKeSSt^ )V'frt6 RiGlO BonY. 

R«b->oduxmO Fi^S. 3iiO aw< 351 IH FvW, 3^S e»W 3ii% 




o 



F.5. 368 





« -F %\ 



(wa 



I 



}oT<e<> V ? ? 9 W R' "^ wt cc,n <X.\^X tV^t skc-« 
— .i^^'I'^J^a \>rCoiiJL^t "it c<JYves]r»aw<J$ to a l«K< 4v«aL<?»o^ 

'^ke sJrcSSeS m oia^ cyoss- Section <?( \Kc )>0>iie>H A 
#( \lie Veam^ onre <Jue to T^ aWe *^ frio^e ^f any cyoss sec- 
lit n dn Aft to V <\»*a 1^ ^ u^. I0 tUu^ w.^t<1tan 6 f? ,wlu)ie 
yy\^nS^^^ i^ ^iMCva b*^ h\e, line Oa »«* ^t -force d«a- 




^""^1 ^^^^^' 



^1^33a qRAVn^ Static 5 _/8^ 

^annywhUe iVs Ime oi action k ap lUt ^r^i Sf<)[mevit6| 

r<ii^U.|>c^ygdn. Si|»iW^,lK€ 6tVe^5€^ in BC o^< cjue 

the ^lasttc sTw5S«S (cv /nl^netl ^<.tC\ ot m Want my %4. 

^>yalc^4»oh ^1 \^t HtArvt mttys^cTinj *bc (^^€^ ry^^'^^f) 
"}>dtti«t 3C erf tUt %e<im , 'Wt may A sf^ rt^c -^Wn^;; 
Cdt/CU^RBUr fO/?CSS ina}iatie^andi the sj>ecia} e- 

^orhan erf th& hcatn cWviiA C0rytsl?on<j$ TiS ^^ Seftyicntaf 
Hit ^ftMCjltmian 'j>o}y^on u> ^^ck Ih^ 'y<\y 'is fxxralhl- 
and tk line of acL^n /s fht 5<fcfMeyft jl<$t nieyilicne^, 
Evwiei^tly ^ tiie l^odu 1^ n4>t of>4 n-jni p»ec6 , lo«-i ^rvwj^ose^ 
^01 Yiv\^ of ouicew^€vue<i l3i<jc)<s (ov yoiAsi>oirs3^ it t>^ov W^or. 

^^^s-rcsu.tV'sihi {oy a.ii}iv/«u jo»V\t »er*«;f<*i Two blocks ^ncJ^ 
y\et lie oulside H>e tcariuO' Surface J^lhc jcmt^ T>or ^vtflJ*^ 
too 3^>u\\\ cin c\i\qh vviltj ti W"! slitVn*^ cv "^»}:>pin^ «e<uY, 



^332 CRAPH.STATICS. }86 

N« ■u rn ' '•' «■ • • ..... _, >_„„ ^-. . - ,1 I. .. - 

of three blocks {IT e<q^U4\lWti4.ini»*\«i<fv fwe -{iyyc^s . Tht 







p. a^O ^ Y^^<^^-* ike {avc.. 

rcU ik the Ime aO, tkl^ ^aHsfyHclioyi Su]ipc2.cs all 



ff}t iorce:^ <:jlV«Vv C'f<>>{7t (jrtC , »V ^»Mpwi»^Z (Xwd |:?o5iUo»it iC^v*^ 

\t\txl. lUcLf. out Couid €a$i|y l>e -f«UK<i 1h <^m qu>i t ^S i)€>vt^ 

lyut'in w<?viidi ciekevii:^ OH Wni e<[u,\l .boly^on , St^ Tvc )irac- 
Uc*e ^We Two loKcci T Avti R* are <:{€HCY«5^1ly u.^JritBU'n^ 

net lue {ti^eci viov Hie ^tcciol etj^^U. °^'<A>/y^K 7o<ijJ«i5( ^ untw) 
^afvij'it w«>] \)< hccessary to u^e arVtlyt^ivy tv%<^ "^SiKcrnS fft^* 

CHAp. is:, 

(:fra^hic<xj ^l^ttcs of Vetlzca} Threes, 
333. REMARKS, In ^eW^s ^oUW^a-^i sui^se^ 

ijucntljy (c«]kc) 1V»t stiff a.rc\\-ril> ^ or %t \Aocl<xwot)< rff a*! 
arcV^vivia of irAOischry ^ wkfivx tVU WAy \i C0ylSi(^eYe4^ |j^ 

tKuS, * 4^. 36 3 ^ tul -for Convcnievtc<2 eowcU v<actto»* w\\l W 



• §333 GRAPH. Static s /86 

l^ii 1<md of *y slim <|{ jorxies. "P P tTt- vvill vc^csev^tjKe 




ijf me o^utwfnl Ttocttons j H tne voIk* •] €)1o€y k«vJ26wl<tl 

33^. CONCRgTE CONCEptioM Of AK £aua, 

POiv't^ON, Any eouil . Wl^cjon. Kcl^ \hiS ^ro |) evly ^dwie ti 
tU moc^c df cansryuctioia^ v\?. J I| friC cii ouU 2>C tff ^^ 
S6'8 NA^cre jrvtj^oKcicvttkle 5\y-<)u'<^1^ t r^ds jo\nW cat b witKW 
jyictioti ^7We»^ Wcu3(i T>< in, e<^uiltVv-4urp an<)eY me S^sUw^of 
jews ^W g^vei^^^tee f^g . 36^. TU Filf,36*. ^* 

ytjq oJ Suffevs a * * '^ ^ 

to %t "R Off rt»e 

Cases %tie >ods ♦>vi^kt "bt in t evasion j<?i v. ^ t 

336'. EXAMpIE OF EQUil. fOKYGON T^J^AwW 
To VERTICAL LOADS. F»^. ^^V [T^ sWcUvc Wt- 
\v\cj Itie atv^n loa3> is not sKov/n^\jul ^HKcpy Ihc i>u«^- 
inavy rods or stxfyvitry\\ of an €.<:|tL'tL\>Aj^d»^ ^ v\}K{tK vwou)cl 

%t "br^^^v^t case , ^^ ygyy 1^2-1 ^^Ifiir?-) '''" cc^»^le -{hI:- 

ri<JH ^ <>-)^ '•oiv1^S W<3U.1(i ^^^^.V^ ttSC ec^u^VNb^Uwv s?a)»^e . 



^<&ee r^g.36^. The ruf,36*. ^ 



^335 



QMPX.swncs 




IM 



A 
A 



S^oic i^i^^fc tUmdi 



B 




QavCa 4f¥t<. Wet* T^ P^ OfiJi V ^ Au<i Iwo ^oWiiWiVit 

taffHiv^ofe ;jWf *ff oi^ <x** WJAf»t«*\To scaiCj f^ ^ isiii/ f^ 
e**4 to cnd in tT»<^ order, ui cm s^Wfi^ any ^)e 0^<h^ftir 
fre roiyS O I ^ Oii ^ Je« 0^ a fcnrce dv-o^Tcim f ike. *T*5 a%«^ 

ondl d%v%<Jt. tkft 1d<wi-UwC mti X ^^'^^ X\3 ^^ '^*'*^" 

A {a^^J ^olvl m fii } a hi^e ft fe O^. \ to mttrseef T 
tk. Sorvte Jxjmt i 'y TVr^^k a H tb O^. !^ a^ui So on,wHy 

A8 is 1^e*^aA>u^mtMt-)rrt^* or cio>mo -lin<? . 
gon vvi3ul<J result. /\,s ^o wKUntff^ive iir^^u^ tucv«*)7e7*^^»lDj^ 

er ston€. ^^tvck o*" oTVicv stru-tCurC, ^n wWv^ iKe l«t^€ ^^***^^ 

in tqtxXi thy^uv^^ . 

336. USfFU]. PRCPFPTY c1a«F«UllL.pO.L.Foie 
VESTICA). XOADS. C P'^T.f uW «»*• ^" § 323) S«? 



§3 



30 



CftAPH. STMics 



88 




Ccrtsrdo- as -^T^e a>\j n*o!vvWv c{ c^mseciAve se/jtviotJi, or 
^A-^. an3 Jxn^totrS d^ ^c ^ ^ and 7^ 

ftt or<iev to «wT5kkv To <ovt5«i'« 

er V 6 6 7 ^ «i jW< U4y» 

For e/^-uil.jOcconllvv^ to SiaSu^ ^%t lines df o^ok of *f 

"j?^l m 1^^^ ^<Vi« c{ acTien cj %t yes*4lajii of P P. a»«ii 
P ^Nc.xjf l^e kict^s cycctorli*^ at ^c inTcweMimy vertices . That 
Vs 1^ ^xmit C mud Vetk fl\6 VcrtWal conlattvm^ ft>e CchIk 
4rf <^«vity <^ tttijse toa4s, Smc6 FKe Ws'rtiVi <rf tKti vcv- 
Tv«»J must "ht it\^tJ^€*^d^ri cf ft\e ^MrCiC&jAy tc^yul , ]>a'K/<^vx 
used ^<3tny a^y (^dolled Imes ^ fij, ^(>^^ fsr^Ke S4*ne 
1a*4:^s wM ^jVe %ty sa^e resu^ Mcncc H>c vorhcal CTD^ccJt- 

Q-ieAMS AJ^D £Q\)\l.\%R.?Ol^CMS. (^ vertical Ub) 

3^7. RFSUME CF CONSTROCTIOAI.F^. 367. ^tf. 

vevTi'cols A^ ^3u*Jl S 'jtU wUU)^ rt»e ciWV*f«yTts ore. to lv€ ^ 
v^e \m,y <?ff <\ l^jA^-ltrie K.*.^, ^ ^ tb.k^ any Cotiv4iv»»<»,^ 

F«>^ ^ curves }>0K4ma e^uJJ t^ol>?<3on^<xS5a>v<e 45iv,y |xe?vvt A 
»Vv ft\£ >€nrUcai A ^ for ci»^ ^uh-ne^it ^ £iwi^ divixvu Tli€ SaC- 
Cc^si-v!^ SCi^mevits AT? ^1?C^ lie . o-c^{>€cT\ycly |>a>oil)el te 



% 337 



<SKA?K. STATICS 



ifiV 




Kow ^'<Kiva AS, coHh^^ AB iWt aU*lm«nUiM>e ^Arv<i a 1 1| 

OfvlKt loouduVne. Tkis 

ENT OFTHe LOCA— 

i-iv.t ^nfc Twd p^>t*/«ns£^V ^ iwli'' ^ ixu*<i V^ zz "n^n.H^j 
-wVivA aye IWt, vorfical Vri^sures -wKuU two 5i-<-fc}'ovf*. »k 
!^£ verfi<^ A^ <x^ ^^ Vv^g^^-^4 sustaw ^f{ The cj\^<Yi 
\y<3iA^ TesJedL or\. a }urrUi?K>fixl ri^wJ "bar as t*j Fw. 366. 

■ , _ I 1 ^ p«<nc r\ wt *vt<s^ ttsc OHV Coy\- 

o. ^ jvo*** O fo H>e leoi lm€ ,"Htu.5 4w«im» Hie "Ucui-KH? 

SSo, THFOpFM- *f*ne vevtieal <il4menWt>r»S c( ccmj fwo 
e^^ilt^rr^um ^cly^yis , dr-CLum % tnt same loads ^ hya^- 
o^hcOAS^ciru^ ahutmjrnt verticals ^ ore jnocrsely prohor- 
ticnal to Tktir H's (oy 'hole - distant es^^ V^ktr^y^ 

6^<irt^tng fci^«-«-a.. ^l-y^ons ^ |e>- t^e ^>m€. loads Avoi vptt^^oifs, 
frc^ % 33? w€ V^o>^ 'lWt Ot^' h W fo AS ^-^^ On' 



§ 338 



GRAPH. STATiCS 








^uui 






■A 






• •. -:' : 2^ :t H^ : H '^U SA»^e kvlia <.f 

l^ttrof i*K«y -ftftv^^y W aYfUitd to ^t vcytual inteyce)>t<; Jk^iwy 
(t^ If Fie f>4Ae o{ Uie |crrce --(iiA^am be mov&a alonc^ 

^Ho^xi'rt^ ccMsWtly V^YtxlUl U fhe f^rm^vlme vA/V^He: 



(SRAIPR. STATICS 



IL 



; i ; I M 



§ 3¥0 

ye.\\j StraU v/t(ti in{u-iiVeUi s^-H^atl^ 'V».<rri^&*-Aal ^Wu"t'S WWf<»M 

ft\em J c^«nvj e,(^u.UiVrium ^Is^^o;^ y€,(ic\M^!^ ^ LiNbAR ARCH. 

Uv^cx^Viko^Ay \w« ttfin *vjt di^o) w«l\ tK^sC JiT{tnii<\y Sfvie<H ^Qods 

wnicn ar me Sum 'i5f fK<?$e C»»vc[^oS4kj 0«€ ^frouL an/^ iV 

. . a|>|ilCeci tkvo^k The eenlVe af 

♦ « djent to %z cuyy<t ^ 1Hj6 A|M^* 
tr. J "7/5 ''^•k ; %\x9rM\Q lihear «4in?k ^ani ^Hdi- 

bu-Y^^seS, Sec. f^»^, 37^ Tke Su^ct^s/t»€ 1>0{r\i^ (j'f l^i^M. ' 

vUiori l^tflween "Hru? <jy<ju^s, TViU reAAllon 4<>^^*v»«. HvH tec- 
sfs <5f ikt <^»w^kl<ix\ treatment af vou-^iojr, <5r VlocVw^^, 
arched. 

3¥K TO PASS Ah eauil.POLY^OIv TMRacc^^iy 



P. n P 






■ft.' 



flr-i-fi- 



of loct^^ ft '^5 r^" 



• 3' L*. u ^-^V;,:: 4 ©uT^a^ ^f \\\t had* 

b«!w«t^^ lt>e VtyUcqJs <jf lS%e U>^ tviro, Stsc K^. S-Jo', The 






"WlHv 



bKAPH. Static S 









il 



-n . Dra>v ->VT li 'to ^ A, 1 nc ycic cf i>»t rcoU*v>>;f 
c.a\ [Wm^^k -p. Tln-c VI ^' 'i'^^ re<^<^^^i e^cu 1 . bolv o o n 

it>-.c W«^i? |:,il:s •Wate^s^-c^ron wtin 7i' T ^n^^-e^ C H-.r C'^<,fv^d 

.rrc>VY<-,p«rrH^-^-if^ fcOi^^L^Vx/^-jtj-Ou^ ' btiiifs^vu-'v^'vtJ' at fell. 'f^rSl cc • 
use pu55 invoijuja |3 C(nd S; "tt is nj. 4r^\^n »n t- 

:3-^-*2, SYMM&tkicAX.- case crTHE Foi^b' 

Vi/4,h^t- rin^^^*^, on. H^e nv^^j^lc v^-Uc^i \>4v^€c- 



,4 T,' m-.L^-I C'a'i..v ,.-• 




^^ Take i^ C3>^r^r.t 






<'U- 



C;;8,Ap>: . :5TATt 



H3 



\Hc SCoirv\e.v'^i ca*rila»^v^ %.t "JsotWt jb 'i-i^u.^. fee Hxn-u ch ia( 
-c^ix'tU ho1>/^on. A il to C/\ iT^v^iu^U i IS ltv£ fwbl^ '^'^'^ 

§3^3, TO Fi(v/t) A ^Y^TE^l Of lOAD^ w^tF; 

f4 ^a\)lh^moJm. riG^ 373. tei As w rtie <jvvc^ 

; ^ <ibww*^/ a 1\ to 

7^i\ r-ovv bA^v V-^ deo^ wUK «\». t^k^ k-vtanw-pv ^ l^cj 




€4^' 



I'Vi 



s v^ 



ASCH£S op MASOKRY 



\C^:LL 



CKap.X Kxc|'W{ /Irches of }v(a6om>/. 

vAuck H>C faces arrt 1 "to ^^t axl^ cf %t, c^miv/cal 
Soffit J cr ur*d^ SMrfa£c]) ttiC S«CCCS5We Vlocks ^ermivtC' 
the a>c>i~T-mj ctrt CoAVeJ ^ >ro\A. %%o\r^ fvao^-SvyayS 1 

|V\c^$e of CL cHTCcJUu- coxVi ivo cmt-> t^6 axlS «5f 1he cyVn - 
r«x.<i|aJtvt^ J01V1I5 l>tV*^«n the vGu-'Sv^rrs av^ ♦vuxi.e "berWi*^* 




TKAD05 , TKc i:^ru€ trt'rtte Sat^e |>law€ 0,5 Hie I'nrrKi'- 



-1 

J 1 



i 



'N, 



^3^6- MASOnBY A^cH^S ?'?-''■ 



TiOCtty q.s an ^ir»ei^t <jj siolbii^ in. aycrr<s> cyf a^^^ cov^^<<^eva- 
Vie S-ire ; m^&u/^W "K^^-^^sciixW n\c>nx< andt mm jcrnls o| or 
4>i^<^vy xrui^\4iy can S*nie.rim4rS W dkjpc**^W <3n . ^'tcl'to V? ^ 

«.40-%i a^id To ^iKi-Aic? vx^ovi eoJ^ BiKev ^ a6 oVso ^ IKe \»UcV; 
-Crr-m, , 

3-9-6. POINT Of ^PPXIC AT 10 K afTHE RS -- 

mlt a^a Q.L ^><-oc<:e^S!v<i "bcHnts erf a ^^omL y^f^om \)\^ ^vi- 
Ty^j^-s^ W^^dL R>e exF^nodes ,«rv vice vers a j >!>>- tKe tnrcl ? n - 

ate <^ TUe rcvilve er( tjravtly fs lUe 'Jjomt es[ <3A|)lf.^a\»on 
^ fr <"- > g '^^-^Tra *^t l^r « S S ijOf g. . TKuS fxij^ ^^^-^ & ^-"'^^ 
whey*' ttSe Ica'^L cotv.^-vessioK ^$ Sttj, - y^"^'-*'-'! 

]?cf5^c( fa exist **t toe mfr^os A^ \he /^}C%'S''j> 



%3¥b 



M/VfiONRY ARCH£S 



-/6 




value at "B ^»n lKc extraudos . in R-^f. 

376 ^ wWcve "H^c )>v«^uv< }5 rex? oit 
B^ ^vv3 vuYi e^ as TKc/ drtiiwuJks c^ a tv/^ 
giHjU. rtie Tt«*iU*Mi ']>i'e5Suve. ads TW>t?wfk 

iKe joint kh^rti ^fyvtvc 3. Hw«. vuk^Kx The 

]3?t**^^v<: 15 not xe)r6 <»t eit^ey ed^c tUt 
THIRD of tKe }<U»^L 'WUtrre^, if Hve re 
Hiird^u -shows mat «. l>oytj<>r> /\rri 6^ iVJe 

j5mtjScc Ft*^, 3 7ft vectiv*^ n<» [>^^'*-^ 

Ji mu^^t h^ u>id«Y5tco<i ^al tK^ j«vi( surfaces Utxt 
ckatt .4*^^»<tt^-«rc rectoviAles ^S<^^ «A^« wl^c vW the -fwuV'S 

3^7. FRICTIOM . B>^ cxl>€rnnW,U Kci^ Ucr, {.Mna 
H>e au^ of ^^yictiin ^ 5^e ^ ^^O f^^ ^^ Cohtii^eMS 

efficient df -jViclion »^ ^ - "^^v?.30*' , >ievtce ^f iKe di^ 
see f^ . 37? 

3^8. RFSISTA^CE TO 

^\t limit ^vi'^, tt^e e44jc <5f ft\e mli^le 1VnV<i 





^3^^ MASONf^r ARCKSS t^7 



rT^fruW^ the mcavi ]5TeftSay«^rw^A.stlles5lli^M "^ (^ 
(^ ]xv umt <^ aTeo. 5 

C Wma -H?^ lJt»^a^e 9*esrsiAH^ "To Crushir^ af 'frc tviatirv- 

*>itte^ alfluVm^ <|W^ PCOT 'ttuclt' w\)l ^ way 5^)6 ConfSi'd- 

tKe ujTtts em[>W^^d tf> 4{::p^»*»y fr)« aWve test* 

EXAN\plf . If a Jo5wt Is 3 ft, \>y 1 ^t^avi4 ft.d 

>«s*4rtavtt -j^rrs^^A^^ ^5 32.6 tans Hic me^^n "br^ssuv^ 
J>eY- 6Q, -foot <s 

wWk Ji tnu^Wl less Ikcin ^ 

fjj cr( C ^or m(y5t W1U»^ «f^*n€S^ see § ${)3 . 
At jomfe v^A-w^e lh£ ireniWit ^?rei5urc |aWs at itid 

ecf^uiilto 1>^ rwcan '^ *• '^ '* S l^ut {ov 

$»<q€W it Is Vest To assume tViot att tiyvte<; ^ (^{yoh^ vkiftv- 
M\G| IcKxd'i^tfv v^Vroijon^^it irnay move 1c 1^6 ecLje <rf lli€ 

3^^i TH& THRK CCNJOiTiOAfS of SAFP 
Re<A{>itJAfiKtf the i^e^uXls of IV^e «|ore^oJK^ ]^av<U|ya^/j5^ 
tv>u^t \y< $<itilsfi4?d «t eve>7 jo^^i of ckyc1^-v»wo av-d |>tev^ 



S'H'? 



A'BCR Jf MASCNt^y 



ffS 



\^\.) Th€ TTesuCtWnt jsressuYC tr>ust \^ixis wtlt^i^ tk^ 
(2.^ J Kc rcsulWvt "d^res^ujre t^uUt not mok^ on amf^^U 
(3^j The. tncAn '^ytssu,r€ )wjr Mjwtt tf| area. »?n fite 

360. TU TRO£ LINEAR- A«CK^ or Sp£ciAL£- 

asm F.-j. 39 j. I I J I [ |lrlj I I I - 

frit -ftrst joint <^rui D m^ I--' l**/<i\>^'^ 1 "n/^ \c**m_ 



point ^Ip ^ in fric crovwn 



. - I • V 




Tod^ (^not roHn^ were Vnsrt^edl at A_j^^c^ fi?c«^5<5 a5 
td Se^aYoTe line arch- atbr»es sU^Wly ft»e arcX w^nJcl -$Und^ 

%t joints w»»Kivt itie cur^- rm P ^ «Uv4i \f mc tn^l Tods 



Tn olVie7 Avdrds^ if avi avck slandi^l^l may W bdisibie to 
(i^ra^fl/ <X <iveat/ nuvvtUcr ^ Imcav arcWeS vvivn.m ft^eir 'iMifi\tb 
^ the aY<^-T\«io $mcc fttrec yot»>l5 <i^tVriT;tn€ an c<^<al»WitMn 
l^^^^iaou Qyr linear arcKj "(or <swe« '\or^d^ * 1 «€ <2»w<w"n»4% Ji-* 
T»5i2S tlijfnj WHICH. l,l>/)^Af? A?ecH IS rXE X.CCOS OF 
TH^ A<^T<^'At R^SUxTAxiT pR^SS01?es AT THE SUC- 
CESS W£ Jc)^^rs ? 

^C^^n^^mVio "ft»e <t<^n-v*M.a as an eWstre cuwe<3 beai%^ 
m^er^ xn Tlrm ^/^rS" ^i^. iV»t "blocks at iKe s|»r<v%i^ivuJ -llf>>e. 
core i7vc»{>a)>ie 0^ UAJnTitv?^ A«wi Kowimj $ecx4,i*ea a c^oscjit 
oi cCO. J*ln^s l>€ffaTe ll>e cenWrtr»<l iS tcwered^ 1)ie Tvioit fiat- 
V^"farli:jTY cirxS\Aier fc> An5 <>tAfe4U©n is J/V^n tn. "Pro J. Greene S 
" ArcWes '' >, 13! ^ Wt iKe 1e<iuwjL$ a^fyJ^iTations tiiere. 

fc\}v|'*S qr^\^Wi<» TYiet^ci (j ^f evj C<^»^5WcUoviS in GvajsK/r- 

a iviueh sim^Vey yr^ce-i^uTC 15 5u:ffiO«nUv^ exact ^or ^ra^liCa) 
"bixr'poses, Tki^ «a)I new L^ ]:>rcS eviiei 1 

'AfKev^ t^^6 ^iosbt; TJocks Well ot 6^e ed^e , f«>. 36^- 

lj)y\l/ // K Ccuit dtlicr And ore tnirn ^r«xflLu.a.l\^ ^r^ssecl 

suy^oii^ cj^ e£>ntact Wt^mes W^v curui laryeT fr«TM. jl^c c©m- 

CT' /ffl'^\ cint V'^'e.S^^-*^^ Wwc^rv hne WocV S , first <x\>- 

^^^SV^^^ ]A*e4^ ci "the extreme adae \r» . \\os »^ow 
5 >i^"/ ^ oi^vTxvtcecl n'C4avev iKc micldle of me }£>iV't. 
vvitix In 45 m, view we mokvj r€CJ50MaV>l« ^€- 
^MXtL t^fi |oVi<i*»»>in<^ Irieovy ^ %^ location o\ ftie T8o£ 



%360 ARCrl OF MASOKRY 5too 



^jvKjd. *^ Curve ^ Vr<:;ssccre ^* J trt. an ccy»U tu^tx <^iven iocwl- 
^n^ ani w\t?L FIRM P\ERSXWbelK«v- ^^e >'eYS ^0^^ yeaViy 

35i. lvOCAT)OK OF THE TRUf U>/£AR ARcH. 
Gvcintel tKat ft\e vouss^irs Vavre Wew cLssclv/ fttteot fo cack 
&1Ker ovev'lVte ccnlervnQ (^iheeU <^ lea2 are som^ft^mcs aS€<} 
tVillHe joUvfe to >>tak€ a.^«ff<r <^>^rnU4lw«i of ^rc^Utx^y] a**^lW 
ISie 'p>ers are -jirm 5 arvdlK^t ^e ord^ can xtaw«? <xt<iVi wi\\ 
out \Ke centering ^ %€n iV% w6 TnulMol c».eiCcn»r»'^ciatiotq !>«. — 
• Twe»n ft\e vou.ssoiir5 ,as ike ce4^W\V»J 16 Uvuerci^me rciuU- 
(Qnt <5J %Q^ WcSSior<5 dislriWre^J over an\^ jotnfc Jfot -first 
near ^\\t ejctir€ivie ciae of the jmnt ^oAv^cutces ir^eorcv fe lh€ 

36tpRACT)CAL COIVCLuSiOMS 

If |orA4tvOt OrcK and. loa4tvva with, ^rrvx p?evS ^ <^v*. 

<sf \>?e hclnlis A ]> Jtt<i B Fiy 3 8lJ enuVel^j wltKm ft^ 
t>ui t^e 'TtscciWrLt 'pressure dt evevs ictnt wj\l W wimi>t 

aa Ihe ml^le ftikVd, matvs ftxa'^trt^^-* one vuhicVi n^ost 

bol^Qori can Tot <h"awn *vilKiri tKa ml^le tnivd ^v4 only 
one wilkvn fti€ fltrcVi -Ymy ctt oJl^ Itie oirch nta^ slavxi 
but cVvj|>|pm</ <Kv\A Sj^qwlm^ are lil^^lv Tt cccur oct (h<S 



§361 



ARCHES Of MASONl^Y 



_^?gj_ 

\no rattst te c\-ian^^ed'^ since, Auliou-jH lt\o <xTrcJ\ m^y 
starve?. ^Ivorv-^ ike re^/^tivtce (>f IVje s"j:>an(3t-el wa\\s ^ SucK <2_ 
sto^Aily -mUMT Ve lo<ji/c<l oupa-H as ^recanous Anxi nol, Ct>ur< 
t£-r»c«r>ce<i iV any 1ar«jc Jm|xrrli<»nt &TYa.^Cuve , T vcr»/ l>^ - 
cnxepSlsj jn -St^iaU circles of WcW avi3 sfond^^i lV>€M^ occur 
in )^iul<Jm<^s^ ftie ccrv»cot ^^ So tetnaci^us iKctt me wKo)e' 

AVhe^x fKc '^"tvHt *ine<iv artk Vuas once. l»f€K deT€VJvt»M«cl^ 
Ih€ cxy^^oujaL <r| tne xesu^vo^vt l^jrcs-iure on awvj joint. ■•$ cji/- 
€vT V)o )Be lev\^U7 erf i^t 'Wo^cv RAy iw 1>>^ fovre Sia^-jr^m. 



ARKA1Y6EMe?srTofDATA foR CRA?HiC TKBAtNVbMT 
.36*3. CKAI^ACTER Of LOAD. I^ mosi Uv^e k.r<)e 

constat occlw.<=.ivic\^ <rf m^$>or.rV cxb To the rood • way l^ut 
*^a>^>alW <3[ eciyfli -JO\mo oiaCYt )\yt maso^rj^^ orce{)t cd me 
"^cues of \he OfcJTck MiKoe tVie s^nire^ wai^^ '5,tr^fi^ as 
irelainh^5 v/oilH to VioU tKe earthy Fia 
36^. If tl^e xnlya^cs \<> a Kolf 

tjprmtjtnO'-\ine k) .about ^0 or rS 
from V^-»e croww^ F<o. 3?iS*^ jo Ht«tt 1he 
jacvtion tff arcU y»v\^ tclavw A B Ivsay 
be cc?wSici«Y€<i a.s yanrt o^ %t a^XjCTrv^tra ^avi<iiKi<$ AB I5 
tK e v\\ tu.a] s|p rxncj { n^ - \ i n 6 fo >' cjWjiV^ i c tv^at m en t - 

iVte ViCU4vic\\eS <^ rKe mc<i*^ <?cv-ch ^witH carlV ^Wted c3- 





^38y 




% 35^ AR CH£S Of MASONJRY 2o_^ 

Xn any ef ft^e |»<cecima cases it J& c^s- 
LOrviAvy To cijr\S4<3lev- trux.t^ov\ ax^oM.vit of 
tne \5onc)m<^f erf m^ st<iv»es ik tt^^ avck 

% 35^ REJ:^k)CBX) XCAi^COMTOUt? . 
Ir\ Hie cpfa.|>Wlcal ^ISCM-Si>rcn tf( a. jsmr^sM ctrck We ccvy-ytS^ 
ck\ayvi\^a one. FOOT tt^tcW ^tVjiS ^<3lr«^vva. To€iM.or vevtjca] 0^%^ 
*1 tc ^e coi\6 o^f ^7e arcW '^ 1 .e* \Ke ^<:<m\»^a »s {} to %e 5^»». - 
drel vvaHs . For ^voi^ii'vcOQl Ireafrwie.v^t e^jtcal areats <?f tV>e el- 
evcxtson QljJL Ft'<3. 387j[«T^^^^ Y€^TCSe>it e^txcj vy elcj his , "^l? - 
^-prp-tx inA^ tiie matevtol of me arcK-nW asA 

E» LOAD-COMTOOR''^ ue. Ike i^Ma^Ww \me ^A M^ ftic 

scvnts « la<M^o<^o»^o<-c^ Icaxi ©"f tkc ^ciiY>e <]i€v^ty as Ike <\y<k- 

36'6'. eXAJViP)-H OF 
RHDUCFP UiAD -COKTOUi^ 

Fvsv, 368. G iven an arcV^ ■rTn<7 
T^s. ^^ptY ciA^oiC ^60^^ w«ik o<. AtaA 





F.-^, 3ft9 



til (k«tavr.= ICO)^ 
dislviktcleol cxs m "fiC^»*Tf e . f\x. It^e, ]3oinl *^j,cyf Ik^ eicTv^i- 
^^063 tke ael>(V i' 5«et of rt^'taW^e is e(ju.;vaWi^t To c^dej^t/t 



§ 366' ARCHgS OF MA^OMfeY '-^03 

4 [ «[^ X 6 1 ^. ^. i ft. ef <^raml£ , ^^W^e iSit 6 fect 
cf e^rw IS c^o^vilent r© ra££- X 6'T =, 3,6' feefc<ff Gran- 
ite. }\<r^cc\kt i?^DUC>^'^^ -^ * 

-{est. Tl-iot 15, {or^&cycval '^^(JinVs df ti*© arck-rin^ extr<3uio5 

H^e eaY^k oriirvota \r> tKe rolio \7o : loo av^A a<I<1 {tie re- 
5«^Y^ J selUv*^ eff tWe s**tK v^ttccJlj froivi tWe |>o*f!t 1VV The 

t^viatnite Oh e -foot tU *'(&!<, Ttu5 
df eou^sc V16W includes llie 

Citti^ Wici<^e rti6 liVe^^odL*^ ("a Train ^ WomoF|V€^^e, 
J. ^ {£. Hike an exlreimc easel can n^ W <iis^e^«a*Jeci 
cikJi -for eAd^, <5f ilj yo^JjVni we Wave ot "SeJ:y<«vciTg i^P-* 

t^min <5| l«c<M^otiJ«5 w<t4aVi*iy 3 ceo iks. Wv- rtAnnlv^ 
l^ot df "tra^ C£JVe.yS owe Wtf ^ ^^^ ^j^arx, iTttVfoYw^y 
^4s|r«Wu.W Wey^^Uj; ^r fW wUlk^ 1? ft^ iKi's ^Je d[ 
Uo^j^^ Is e^u4va)eHt to c\ tr\^ag^n^\j \ocnA o-f one ^ooT 
■K«i}K i^%*<i ^$0 lU. 1,er cu.k'ft. licco/^m^iS J *«£. ik e- 

Sidierci.. Hcvtcc -frovwv f < <^ . "J^C we obtain Fw ,' 



%3S7 



ARCHpS or MK60NKy 



20y 






E OjiS.- ^ 




^ CoWXOVR 



36'7. PJERS AMD ABUTMENTS. Ik, c, ^eWes of 

e(^ua\ arch*:$ "ti^e "Vi'ev \jerween Two co>^s(j6uIvv;e av-cUe£? 

lotAvs s^»^|>i^ tVit weicjVii -a] tkti Two acljcifeht S£)Vl|-o:.r' 
Wes ^ ^Aa6 \Ke l<?ctcl \n-.vwef^ialew above, hte yicv oind. •*• 

<ioes viot \-}£xL^ to be as Wy<:|e as the aWulV>ev^ts of TKe fiv^c 

■VAi^ ^cist t^vc\ies J sthce rtiese laiTcr noust b€ lyrejxxi-ec) fe 
re^{«t rtie ot>liQu^ tKrtxsts of fhejr arcKes wfiliou.L Wtf^ 
'Orvx. rtiC rfirM.^t o| ctncfrtAey arch oh t^ie olRcv Si<Je, 

tdrnavw to n^cikei a ^ew o^ the irtie>fv^ediai"e ]:>i€rs lar^<»^-. 
'.Toui|l^ To ccci OS aout>nents . (nese, <Xre cai\cd <^"-^^€Mt 
.ieT5^\ o^w<i fn ca^e one arcl^ ^-UovtAcl ^q}\ ^ txC otVievs woLc\dW 
leiX cxce^^t These <3Ccu,rr\v\Q 'V>cTweevi VUe SAme two ai:>uiiT.ent 
]:HeY.s as 1\ie "^nst. 5ee .Fib 39-2 , A A' ePc ave aWt.^/eirs. 

Gf?APH.ICAL Tf?rATMEKT of ArcR . 

[>yecediviy l>6i-h5La'bxbViS^ fov <x .aivcn atcW i^vod load ^w< Ave 
-veaavj to "j:nraceecl iv'itlt tVie cjvaf)Vnc treattv»eht ) i»€,,il'}'^. 

>i e c e sS a V ^^ to \re at ^ s e p q vaW y ^ ' cu )u\^^ tvi a. u v\d t?r Hi e il)^^ - 



% 358 Ai^ CH Sj_crj(l A 50 M K Y 




•^N ' ri^ 



p^*- Kai-|«sban-1 



^ ^ _^^__^ goo 

CA,^^E:I. ^YMMtTRlCAk Af?cK ,w. SYMMETRICAL 

LOADING, C'^U''^te^.ly'^A,evv>,<Xnc',.t) oraea<i *• lo^.u». 

LOAD CON-Toui? r ,. V- . > \ 

(^ w\tK <5nV| o«e "half (so..^ M-»£. le{-!: ) of 
111 Q ' av c h c\yx3i \ocui . 7)\M I'cl € Th I s s t?m ; . 
t\-rr\\ (AvA.a W<J mto Six oir^^n diuiS- 
iipn-^ Idu veyltco.) Unes* these ams,6K5 

(a. Co»av;ev^;evAw;koU. v.urv>loev of (^et^ eJcC€^4" tl.e la^t On^, 

f€venl w;a\H 13^ (tt^e Vcfv,»aantof itifi Kor,^ on lal a, ^TaH^t- LC) 
The wpUjUt 5-f m^<,onYX^ m ccic^ awUich i4 ^(^Hcxl io 
(tW arfa of ^^w^srot?) Xr^^^'^^ til W<v^^^e^ y /V^e^^ltl cf ^ \ 

^.xa IS 4hi,ed rt^.Tou^U rt.e eer>r>e of -^avUy of ^e <^^ws/.., 

.^^^ 6 •>. & JS ; or i>:^ !,S7^^. 

r: Oi^U. ""^ v/^^'ei^ht of liie ]>e4ix<)c5Vi t^ N 

^'1'' ^ F^cj . 3?3\..v.a Us Vne 4 a|^i;,4- 
tjcn (jKrou^^ centre ef cjrt^vily) iv.<3,y V>e |<j^^^ 
\>j/ cor>^V)mm^ rcsu-lts fcr ^Vt€ ivvo Vv^eioi'Jf into 
vuViJcV it j^ di'Nr^aed by a vertical ^KvoccqI^ T . 
New consider A , Hie mU^ . • • 

Ale }>ojnt df the cj>ulineni 
]oml,<x^ tire sW»>^<5 ]><}int 

fovtKe (jW«wloA.am^^^i<Kd^y^- A 





% 36^5- ARCKBS O'F MASONRY _A^^ 

" i« • — ~" — -~" — ' — —————— — — — — 

"^ ^rti6 hTt«d<i)e <?f "Hie crown joiVrt^^"^ H\ro«^Vi tV%e r^UdJeof 

proceed as bv § S'fS.^tKu.S dcVerrvwfntVa ttie \o\^^o\^ 
A > {or the Ka^- «rck^ 1>kxw joji^b m 
ill e arch -VrTM^r Ihrou/^ ftvds€ |>ouJts wk^ve ^^.^"f^ 1 

CHX^s ^e^aroXitt^ "five obvi^mHS/^not lVi6 c{^»^v- ♦ \X 

jeiVVs are ^ut 1>^ B>e S€<)^ents <?( 1^« *<JuiIu- O^ ' 3? 7, 
Inilovi ^>oK|Cj|oi'V Fio, S??^ -sere tKc W*Ji o| a|>|>Utallevx »k. 

w'hu€ tK^ cwwoMvit c^ndl 4rrection of coci^ sjxcK |)r £1,3 were is 

A^c»v "1^ -j(5^ Vt^3 sHouU W. juJU!t4*usly rrforei(\t/^rtivvi !!>€ 
rni^^U tVirvd") fe -Jtni if bWAsle ciii^v€«r arcK wV^TcU Vee^s 

^€ !V?'i«iih^$ cf >Ke £xrc^-rm^ ma>/ W tx^reo^ecl <:i the 
oWUM^ivtt C'^tvtk^ <x StvoJ^ev vw:v;fase Wjord tKe crown'^ 

TrcWuIiD*!; or airri>urtt «f tnC ^c<3L3m«7^ if a^lcwaUe I'v^ay oa'in 
fb»»^ dtoject^ Tf but one Imear avcVi can We drciu/n vvimm 
"W naldlle Ikirdt ,^ tvux>/ W c^msider^d tSe^^Vuje* one 'if 
5€Vev-aL^ tke OTrve most nearljy CcJ^iVciAJviO witW fti€ mi<i4^es 
<yf ft\e \fixr^ { see § § 35/ otO 36^3 {4 So CfinsicUw^ 
%Z^% Co^e It 

CA-V- ARCH',(eLv5^ a.rcU w\|W^»v£ loa<i Covev\vva one lialf- 
s|><xn c\A in, R(>5. 'S'lO an4 ^^IJ Here we must cvJel^vit- 
"lu jx-s^ <\ ^iaU 'force cJvoujroiim. ^»a5 "th^ -TuiX e^evA-tioH of 



% 38f Af?CHE S' Of MftSOKgY 



07 



?t. 



y.mt at mAl 

' m;<i<ik o{ frie Cr<>wr» joint. \ Iick V>v/ 5 3^1 (^t4^> '^n ^■^i'^ 
Wvum Y^<^(>yy (2>t«Loc\meav anrcW) IKroco^U ^-tfse 1W<< ^^'nk 

ISe rrvvJulk Wdl, Aii> fe) tt\e •'ivvAC llvte^y OcrtV' ci^atw^i 

0^ fee desj^n jJc.., i^e sa»M€ r€ma>lc^ ^t*^> ^^ ai^eoitf Y^"^' 
en m C^Se I, Tevy {re^^iA^i^lj H V^ hct s^€<t$$<:s:vy^laww 




-rtA 



THcin X^e -^rr^^iVuxL -^t ;<; rv^cil always ajj^c^re^xt fkx Mt^ 
?*vsj>*i<^vcn . a>U 1ti& ov><?- A\yeaJ)> iravA/n (jj wiiW Wi^^^e Hx»i^J 
vvVU {uy^sic aK:cWs Si^'fr^^**'^^ oic^i^vole for iKe |>reSS<4r€ 

CDvi7«^eYeA «&at»6fa^:Wy until it rs asrfrtotn^ IWt |cr ^^C 

(L) WliK»A tiFve m\dSt Iturcl cf ttTcl joint 5 

(^^^ At <^r\ avv^jle cf < 3C w'llii ^r\£ nox^al tc J<?tnt -^yfact". 



$ o.:. 



A*^CK!?5 OF MAScK'V^Y 



?oe 



ac<- 



§ 36#f ASUTMEKT^, Ike ^UTf^^.i 5Uu)c^ U a>,^f. 

7AiitS$. The |>rtl^5M,r<S of Ihe 'bi^Jt^t VOiM^Soiy i/^pn Jt (cok^ 
^j-^ftvcW^ oiVrM^^ia cno^ -foot thoiV) 15 <jw«w* W^ HKe }xropcvv:vv 

:)vi tke a.mi»*^Kt <XKd iv*f elt^.n of the YtScclto-wt ^|^»v*<'c( j^y 




00a mM 3D , c<u(i {hid ^e^ cenR?. o^f<?v^AVll 



3'?'?. 



wrtk J^ «ji^ m€^V' mrevseeluJta D. Tke 
ytSi^iVfi^t X sUotJi \^A cut tk^ %a.^c RS JH 
. , , «*.f>fitr>l "kt-jOKu^ rke mt4Jle ^MYiL (jev^if Hiti rme 

osxe or Tlv-o Vwols £?t ScJ^'sfo^cUvy wUlk f-^in We Jbtamc«!, 
^W« i>k«Ml<i also \?<^ assavtcl IKaI tU <\K^ie;g]D(^ {s* 
less TkAwi 30*^. Tke VuD^xo^^kl j'^jUIs ok^i/^, RS skotJd 
<silso %e tesled as if Hvty wev-< ^ T.^ U>n , tke l6vve<'l Wa 
aud \f >kecc^5ayy n\-^v| bs iVc\mi<i (_hW inn) U )>>^vtfvvC 

£c|uuxv^ iVick V > TVuui 7^ rtie crc^^KiVij. $Tve.H^ik ©f 
itve W£A'c|kt of \^t \o3iv ^c. Ct Co^v5<.c)erccVj\« extent. 



Tsa. MAX\^10^^'> r (^. s so f^F"FiR'~uMrr op Afti^""" 
AAfKH^A/TH£ BtSUi^TANT Pl^e'SSUfiE FAU.S AT AN^ 
Q^i^H DISTANCE PpOMtHC MlXl-X^if j o^cx^H'-? to NaWa-^^ 



^^ AS 



IS'cj. ^OC 



avf ^r<:»|><5rtio'^ia! U l^e. Hues "K c'^i<l, vnt*)^ a C)wa)c..Us^) 
IKvouijIt wWfise ctX« tff cjrWy ^. ctcts . "But (^ ^ <6 J 



If -na*; 



' d 



9 



% 






Co^st IL.I.t :H fall ouiMdie H^e wvU, v<i^c.aot^.€ 

~^TICI (y^ -L c[Jj ^voka mUdlc of Wt, Keve since It^-e 



fiv-eyt co»M|>uk Ihe v^^^qy\ ]^y<ss, )?er5ff, i'k 



li 



1 III ■ ■ I I T ■ I III II 



;U«S 












/8 |/8 






I P 



(ft ** lift 



>.■? 



I 8 a 1 ^ d U ? 



(<i <n. inches,^ 









^■il'f 



4%-,, 






^ 56^r ARCH - RlSS 







10 



1^ ct t'ioi'cI ctcrv'^ii l>earw^ ellKev Sob4-/CV Ibu^lt ujr. ^^ 
|>»('te'3 VikC <\ Xru%^ (^c^^d, fl^en cai)e<^ o\ loracecl arcW ) 

♦ tr\V3ed iviodle of c,^>^>c>>t it \f> Kere Wo^o-seci "to ^let^vmmfc', 
"The v»b fc$> 5u.^][>oSec\ <*><|nr\metvx£a.l «3ibou.t a veyTiC*li {^UnC 

In«vl<^ <y{ <^r^^ trv^s section i6 uWevdoxjd ^o Tc? e rej^rreci f© 
<lva«ne<i GonAftton VMa^cv a load, il'S sWo^C- <AiffcrS 5© iiHie 

nate 'itself ♦, ci^lscj )[Viat iKc <iiiiv» evasions o"^ c\ cros5-5ccr»oi^aye 

cr( t^-)^ «.c\vv«dL axis , Quiw^tK H\e s|)aa. 
.' 366\ W0J3b OF ^OppoRT, "Efikev- exrvemity^ li^t 
T»l;> ma.>^ be 'Vvinped to fts V»er rwjUitk <5f^t* Irteclorvt ts 
ft^e crv^^tcua^y^Kl-line to tM.rn (n ^Kc v^LylliJ ]Aav\e of U^e 

^.o Vji^Mt-i'M , err loolt^i rv!^\*c1\y to tU« '^I'ev ^tVuxt ^Vlfi «»^iv 
tsvvK^ent Atne i& mcaj>a3^1e ©t cKc^vijm^ IPs dliveclioK whti^^a" 

loncjVVie v'llo . oi»^ci of cou-y^e destroys US •naicl(ty^<5y ve5i^{ - 

TAOv^^oyitcil <Xwc<^ *n To Hie ^xiS ©f Itne r'>t> is meanL 
tvicJcvrrtY rxo jrvxove tVi<xvL rtwee jw^cU K»nap^ couAcl Ve 



S 365^ ARCH H\BS 2H 



h 



366, ARCH R\B AS A FREE B<5DY. In covisdfr- 
mn' fi^e v^K^le rtb -free it is convrej^vcnt^ |oT^<jT«i|»kU«l tyfsP^ 
intr.t ^ tVuxt rvo :,ec'^ion T?€ covn.ceu/e^ mcuJ^ d its exW«v4^- 
ities "<f I'Xe^ ^ keuce »Vw cleaLn^ witii. m-ol rvio<5e df :iujb - 
l^ort rtte eiA^ c| me tHI? wAl W Cov^swicreci a^ liavii/to a, 

of rV.e y\\f AncI il^s tcj^voacwl ^ine m ft^e s^^^^e )3c?5ilVvta*^^ 
rv'^.4-oa sk(:>ws FREE -^ 

fixed m Yhe ^levSjWirtt ^ 

TV^e ol'Uty fcyccs ^ Hie p* h ^o 

t^.Y^ 1It6 l"»<3vl2.0ir>tal C(nc) vertical eo«fv\\>otvenU <5| m€ ^ 

J(X€(^ €wcls ^cW ^ rti€5e-^v^ct«1i*ovis \s A. 5K<^le for<e 

r>ot iV.rcrscclivto lVk>^ ei^dl of IVia v'tjo^ WlT euitiw J [Ke vefli' 

avTcl in. G c^w'^e riokt_)at 5(?m€ s/eyU<|.ec( ^i^l^^t^ (* 
( cr c7 ) frtJw lite evul. Mev^c^ tk^. U.tility O^ Wxt^a tv^a^- 
ino^vy >)T-<)\<3V^*Uiow\5 Q^ F , CW^d 3 R Q. ^"ftiC p»er fc>t.iAx^ • 
Su.j»]^cS€aL r<rviove<i, Cc?v»^ bc^r^ fC^^. 1>H ^ <:^<^<3 3oO. 




I 



An This SvsTetM, cff forces tUcv& are -j\ve uaJ<Kovv;v;S Vi2, : 
V",'^ « H"^ Av*3 ft\e d/^Wces e ^v^ d . Tkc^ir «^<Jt^- 
Iv^inaUoti ^y) o^<x\yj^\S ff ftv^i T"*!* IS <^ cirCtxlfty arc fs ejt-. 

(Pv^, ?didig"s >y^€lV»i>^ 3 sec ]b. 1?^ -fov reference^ tfc t^ Co«^ ^ 

O^f TiO ^V>eJ\c^ Su^fiCi evilly oxctorate '[or j^rwchcar'^uv j^cS^S. 
"This metriocl coviS^sis ck ce>nst>u.clvi>fi5 Uozl*^^ *b Ac loC<^- 
liea of me' s)3-eci£?i) eov>M.Ubvitx.»vt ']j>o\\/£jon A*a<i il'S 'forc^di* 
a(jram. Jn c^6e "^e riW is V*vvj€^ U Vke |>i'ers ^jH-^e i^e- 
acWis <5| Tl-ve UHev- act lkvcu.<;K mese VWj €«=> PIc, H^i^ 

ftie ^ndis ofn^e rib o,^ "B o>^^ 
i^KDVv'K (pufxvililies itve d*il>j iKrf e 
ave four^ljui S'X«- ^iv/*^ Hj^^ ri^ The soWl\oH i>j ^v<- 

367. UTILITY o^-KiK"^ SPi^CjAl t^'GOlLiBRluM 
fOkyGONocAj \lrs ^dYc< cluxj2|>ci.irn The tcse <:?{ locaKn^ 
t^<LSe wai now V>€ ;lUfIW<c( [See §33^1 a^^r^irU 
ua S% 3 3R oa*^ 33^ line co<^);>ves5iov\ »»* ecicU "-voc? '^ 

anti\sWes5 r^Switcint of Hne cross 9«Jions m iVi^ corye- — 
^l^ewxc! iwa portion of thC Tseci**^ Vtt^ O** otncy iJroieujwve , 
HiC va3*<t (5{ <W cot^re^sior? Ak lbs. or tons) V^^frta 

t^Ca^yaivi , Sco[>|>osc tViai in. 5<*Tvtc wa>^ (^tc !?<. «3git|»^<^i«^^ S**i»- 




% 367 



ARCH-R^es 



5)3 




-lU o<\iy cvoss-^cAi'oKi cj H>£: vil <xs oT ttX^, '^ki's 

oclivv^ iW fte Vne le^ awi «*f An amount ^v^k ^ Itifi 
P , t^V^rdi wUix rt^« cW tic forces at" 7n ^orm c^^x^sl^ti* 

-free. B«ticf Uk 
iky The WtA<*i<: 
line AKtA rt»t>nor^ 
rvia.\ aCm AS 

Uav^ 2, (tftMd c<>»*,|^) 







|^e<B*j>^' 



Tt !> 1^« > ^*^^ J voVucK <xb}?<Ar m fine Octy<ssioii^ 

coULpc 'A»tA J tKe^^^f-^iear. Tkc5< ftWhc stresses 
c^v^ closift^ as »K S 2^6', ^^4^1 stt. "]», «**«! Pa 
Ore. ]t<. ^ *^«iSi« '»il£i* ^ '"^ lk?'»^ '« ^^^-^ijifc^t 

^, mcV^^wKi^e X i^ tSe^moi^^ewt sf moft«a*' e| Hie ^«c- 
tion aVout Uiai cjravi^ oocU.[Sc€ S § 2^ 7 aui :2^6%«i)»o 

^cxme «c6 (f 1? acted dvr^ctly u^ow ^lAaWtl jjroAoKjaliOh 
<rf ft^e -vilo at T C^o UTevsfct "^c fi^^.^oii^ ^^ shrJwttlK 

^orce clia^r^tvi. is also /'''J* .•' • ^ / ' 

then {rt^vv. mU ' (<TL^-^CJ •> A \^ 

vertical tnTevccjjt Ve- * J ^*"' ^^ 

-free Wo<ly ^w^ Vav<- {rovw 2 (^tawtd, coivJsok^JstO^ r\ Cpi«s^,F 

who 6 >xoiM. 2L(^rvuMM5, a»»ou-6 . -u t 

ihe <^r»Vi^ axi<» df 77x3= C)j wtUave T^ Ct « ^^ '^ 

"^ e 

Bui -fro^M the Ivvo ^nrvaila> ^vcvK<yK$ (^aA.ed \ ont tf tix<*M, 



', 



% 3S7 



ARCR- R\BS 



!??S 



wV«)vie we mqy rewrite tKese -rtkitons «sf«^lows^ittt 

IF THe SP?QAk &<3UUiklERklK P6lY<Jo>/ >WX) \TS 
FofJC£ OlMRAWl HAVE S£^ JDKAiWX ^...^ ^e*, «»yck.Ht 
of <I»v«K tnoAe. oj ii4i^«„^«Ka-«^o^o.3-w^v."Uaa;„j tkev. ' 
(y*. oavj crosi ieclwsn t^ 1fKe Vil} , we V^we (F= ocv^a. ef sec 






■m3[(^<>f IHc^^iifet alcujYamJ 
tt^otr rt»e t<x>>^. liwe <?{ ike >\U 
'*i at n»fc ^weM Section 

, ©r W>J (o^ TKe -^C <i>a^t«»iij 

H (ov J3ole-di«Wice) af Ike 

■frrtxe-dio/JTiMn few Jhe vfir- 
tvvj tWijk U.4 of The v*^ a^in* 1 fc tW bu..ewJt(*r 



(5*e S§ 2S3 ««d 5SfcJ) 



(3.3 tU WlOMe>/r (y( i^e^J 



% 369 ARCH- R^BS SLl(, 

ve^TiCa] m1«rcei>}^ WW ten. tKe .tjW cxn^ s^^cial eOMUiWum 
"^6^. It H tViuS &<en >iow a location d| H\£ SJ>«Ci<*2 

€S 10 oS\ tKc C"n?65-^^Aa»\S of iW eujrreA Worn uridev 

^d^iS ©-f IKe Vtt, -^or yrw^^v ^»ccairib^ , 

1r)Tac4W(w"il[K oBrievS wW«i V^ ^^coroiVl wiiW it^ to |>rtv€nL 
bu^ciAiv*.^ sU€k<^v|S' tn any Y«irt like ClIok^ Cciamri ^ Behove 
U Ike C«ryv^>5«Je <^|>^cal QxrcA>p\s d\ rtv£ Atffo-ent CciS.« of 

arcVt^TiW ^ ]t w%n W vu:re^,Ja>^\ <J<vcle tVft next fe%v |?^ya.- 
'^-qroj;^^^ i col ari ih rrtcTii J 

' 36^, CHAkGE JKTHH ANCi^f BETwEEl^ Two 
ed ^ as CDf^KJKxxezL uAjf^u lU yoiWe Wf^vc loA^mJ • Consoler 
setuW Cross- :^<lu}ltj :^ Fi^ .^07. t*€t 6a *=^ 45 Vel^e 

VjJ A»^^ %e Two «a*%Ae€cdwe la*it^<yit-Vnes^ at 5 ani A, 

tv \i^g unif^TtKiy rfisIyiWreci 1oi*v6ev\UcJ 1Hyw^ huX aye. 

^00 e 5i<ie ov l^c dtkey df IV^e «jr*\v^ly oytCiS C ©r A ^ of tKe 
sectioYt) \^ ttxe s^stevvt <y| -^vccs tviok^ wViat we co^^^ flit 
**stve^s cou^jjlc ,tKvr^^^ wcVveelt y^e sTV-e^s «^ Ike di^Kt^i 



yer Squays mcK ^ so ^Vioi fee iaK/jcvl IjAc at 3 n<»w t^kcs 8)6 

IseS^i^vi Use. tWj T^rw^cnts Ai^hAs o^ tti« 4r^&^ <utn^ ^ayud 
-net en ^e. pe*iU*n m s|>ctce <*( tKis J>ayt flf IHe "rsU^muilxtnce 




Wort ^tWi .'t^A, ^ 

(oY- G'A'f? - d<^)3 CU'is tKe new W,t.^ 4 ^♦^'^ ''^^ 
"fcnre^at iisUnte e ^rey^ A , <iiA< to I^C frrcc t i^^^ tS 

BMt5a€0%*A£l>iCal\y Ja also =r c ^^ •". ^ 

dt. m o«My "JsArt/cvLlAr t«.se]) vw^ l<u.ow ^vohi §^?S* •f*^ 



%36f 



ARc>hR\6S 



af8 



•jiUjlioia in V.0 we "WiXi/e 



af= 



v- 



Ma^ 



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C^3 



370. TOTAL cnKH GE [.\^ J*}^j wTHS AK6J^ BE- 
TWri^N THE EKlKTANGENTSpr A R\B ^le^ore^^ 

fiied at one end (Xnd 
Whew tke vtW 14 tcH- 

V>os«4 to Uc^ Hie Icft^ 
lU own wficj'Wi Wtvt^ 
na<^WW • ^fc 16 net 

Kct *s evihTel*^ %*rtA»owyC <T>cui^ '^^'^t* 

After i:A<JiUj^n>n ttic ^^^]J^ tKi$ Avt^li^ Ka5 inCvcAscc? 

§ 371 EXAmPlF Of ^ ^^ 




Fxa ^0% 







EI J. 



%3 7[ ARCH- KtSS -^^ &., 

4s of ftie Warrv,wcfi^ H^^it "Vl -pX ^ mom.ijf ikc 
Td€ frien loou^eA ('v<r'i(htiJi eiostvir limii^iAd d^«Tn^t:i»4>H ^i^nt) 

37i^. PRoaECTioKS OF'THFj:)J^P>^AceMBNT 
OF A^^K PoiNT OF A U3AiD£>0 W6 REIATIvi^IY 
To AwoTHBR PorMT A^D m^^ fTVKCE/VT ^»Ni? AT 
TH'E LATTER • Xet O "Uc iKe Wrnt w^os< disp^ce- 
\rveKb J^ cansiAeYcd onA B fr»e o1Ker.^int. fC^. ^10 

"Scti^lxriFJed In <xn^ WQi( (Fi^. *ffO) \ X**\ O'^^^^^^^^C^ 

l4o«x3: Will W £aVWd Ax ,tWt «4<^k3; ^ Aj^. 

tc B Oi^^ tb fe*u^ewf4mc 3T, ^ cA»t ) "its «k2«^« 4*5' 
j 4argt»»gnt m ^^ace ^ S<v»<:e net(N«v "B >v>r 3T Ws *v<?v* 



%37i 



ARCH-R135 



3I*T 




"^tfrrvx vxn.^ cr ex loadL a*%<i H^e <:xl9»<1uJ^ 
ii^Wcemmt d[ O W m^^ W-i n«>t s« 

B''5 Ibii^crvt "BT "(or 'BT VmxS h»o^- 
e<l Id oi Vie**/ \x3stl4en C^«>^*«0 ♦ T^ "f*«^^ 

cad m. StccV oi way ftyd^ 6 Of^ BT 
tvvoM CO mcul^ w»fli mevf orujtvvoJ posi 
ttottS J FtV, ^/2 , li 15 run/ SeCK 

A^ Q^ fcu-t -|oy iKis cas€ tf( W^ed ewis J2<>^ i»^rv«4 )V^~ 
?kai\ wrl^e 4x=^ *^vo c<s co*«-i^yc A wiltt Ay^(fcjt,.^»ci£ 

375.TAkUF5 OF ^^"^<^'-«f 

MEAfl RELATIVELY 
To S /«<» 6'4 

'\>et»^ tolWM. ^ ,\ ft 

F«^.^'^- Aw '-^ 

cj ftit d;f{«y««t <-*'^4* > ' 




O E Q C i^ i\ie uH^wii^^-i ]oTrr^ ^yhe-^^ wVOle 0^^ E**1D* 

C B l^ Us j«lFrM. 4«»^4rY S<»%«^ ) »a Ai g ^ ^<- 4A**Jhey ^]wvt (^tU^ 
^Trm^^y, Now £o^<eive tke* rA> 06 fe "{wi^^ Inlo )^s sl>«u»i- 

frtC S^^^ on^l^ cZ^ (^(i€^ev*^ent oh Ike tvu>*t<^ d^ Ike ^«^S 

-rv^te ^'ece OC 1o torn ^Uout C A5 a. c^ve mvoco^Ul^ 
Sarvi€ SwicUl o^U <i<^ -J \\€v*.c< \\it "bomt O dcscviWeS <x 
^tTicOii aye - S V ^wVio5« ro^tlxS s=^ "t^C V\e VjIxStVietiuse 
«r( ftie 7^ «xnd J^ *t ^ ^^^ ^\to^ < vwiuje *\ ts St) c ^dj4 

a. l^^tofT arc 0*0** - (^S-oy ^ t^'c?^^, m.vvKi^H u'^s; ^< 

Tea to O o.^ x: <tirt r^t a^-r^ciaio)^ off^ctej J ^ TVi*i3 
€adrv .^ 5«timi 'h^yi^ b«en oSowad ^ tcim iWwu-jlt /he 

cawed Yivye O^m^^O^ ^^^^ te 



IBm.'C o V sz CCcJ^ .j and 'fYt)rM Si^vvUa^v yi<^^i'-tWan^l«S 

ana ^ ^-"^ 

If the rit tS hom«<^ke<K<s f \\ Consh>nfc^«t>u} ;( ,1: J^ of 
1he veAio} ]>Une of )Kt A ^ axU iU.,^ it i5 a tu.wea ^) 

for >ffeY€«^C. 2 

BS "fet^^^r^r^^t-V'o^ jtlK c ot^m Vemj ot Q \ 1 CT 

TH^Y-PROiECT/OMof 0\ T)15-> f MXcJs ^ 

tnfc-.cuYvp^ 3s ^H. dlevvvevtt of iV^at curve M lh<. *h««- 
<vit of Hie ilrrts^/Uit^le m l^e c<»Yres|)<aKdtHy s^cIiok tK<, 



% 3^i^ 



AfiCH-R\6S 



Qll 



37^ ot. RESUME o^-r»e PROPERTIES cpHciO)- 
IJBRUiW Poi.XGOH(S ANP THEIR FOf?ce IDIAGKKMS 
FOR StSTEMS OF VERTiCAI LOADS. Sec %% 3&S%i^3. 

Two obulmcnt v<r» 
Vjcol^y^ to "(orm «^ 
tic., select «nj 

11 to O .A tV iWcT»ccl HxfcVne 4^, } ^^^ °^ " ^*^i-^j 
««4 ^<5 en u^xUl ^irwally a. WtriO Q.^in Q jK JUtermm^d* 

Xint (^w«.H \*otflis A**4 lo«i verticals 




:> \ ^ 



ou«<l 



I5L3 2/ »S 



^e^cnts Fo. , ai?^ -tic ^if iovs^si^re:^ to ©e noi^ An^ int- 



fttvi "ttie tc.Tn^«*»^€i] ones W^?j%Jr^eints F^ ov«<J ^^ ^ v/»u44 Vc 

<flv«M IcMs^s ar\£L aW(vv>tT»Uvcrt«coJsj ^r^ cKodSfv^ ^t^^^CMt toles 
m l^e ^oTce diagram, ^ One olPicy >$ iKown U H\« -fi^u-irc 
fovivie<i o{ "broUcvv isjv^kes ^ O "tS Ms b<'lcT For aM c>f lKcs« 

tt\t ^o<ii*W€ m rtii^ sam< |>otht 77^"^^ whicUcvev £^u.Uibvi- 



C^V Xf ^^0^ vertical CD \>e <^ravi/n , ^wmy otw "mfcVCe[>(r 
16 (^^ fi^, ^/Vj "f^r <str^ TWo <^ ^e j>oljji?nS */« ka\i€ 

(Jhy TKe " \^k A.^slan^ "^ H ^ <rr H U^ foil fv^K^. %t 
ere %z vertica] covr^^onenTs of me cor»*p>-es5mHS tvt, Ths a- 
d{ eoLc*K 7^|*^ji K. -pct^ ^ each c{ vrtt CDrut\>ir^s^ions fu, alt 
iTi«^\; cOsc) Wc caiV^ fte attjim^wvi reorTionS (^\v<^u.ej fii»/>' 

l^oo-ds . Ho^sft^ flfw-e** \Vie< \V^^r€^ pwiV^Ts we ivi/^ dvowA/* 

« 
376'. SU^)^rt^T!Q^^ (SP PROjOUClS.'S^ot^l.rAteed^ 
no^ U IVeai ^a^>V\l<^a\)y c^>j fi^^^ c^ avcVx > r i b $ ^ Q, jew 

CONSTRaCT(OK. $u|>|>o^« it Te^uivei fe ixAoke fte 
Su.mmaJiov7 Sfxz.A i.c^t^ 5»uiv. the seW^s 



\nCj'^j<3T i^WlraU<?'ti. ikat Two g[ tVie ^^ /z «v«<l -z^ 











H . ^^ ^ 



ovifKe s<^rv*e s-Gsii< <»c5 !lic OC *s ^ tti^t^ the SUlVl>»*»tto^^ •>-?- 



C4^jl 



H 



; X 



• V 






0^0, ^o on. %.^ H Cv^^-'Vtlc) ^ H X FT? -=^ H"k ■] 
376, GRAVnY VFRTICAL, f^ti^ '^t saw.^ cov»4ruc- 

l/on vn FCq. ^LS we can cAtTev^^j'v^e IVie Im^ <?( «*rfioH (oh 

c'jVak^/5tY vevtiCal) ^/J^C )KXv«l)ie] VCvTlCixl foirc^S 2:^ ^-2^ 5 ttd. 

dr loads oucTs ti\yoi*^ C ^**>^ ^^ v^^vHca} m tii^s case ;i1s 

t\-ie fcrrc€ ctiauj-rrxrvt iD^yJnn&le^i t^ tke ^rt3J>€r Scale. It \S vi<?W 
•Si<bpcscdi iKat tKe -zl'^ >-e|>>^^«>»^ forces ^ the X 5 Vev>^^ Hzetv 
Tes|5eeUu€ Wrv avms aVo^l' F, I^ iKfi ^'j Tr<j?T<rS€y»i' "le 
CAY^as of Siv^al^ fmi'te "fvyHeks of ^ Vrje ^lanc f^^^re^we weiy 

<^v^ct F^voeVux^e also y^ .^{jQ ^ ^(^0 5?«c«.u5f 2fe) 
J* "^^T^inlKe }>o'\x)<^on FQ m SK-tk ol |>o^Mion as To 

;<Jvrtnj. '^►WCb /^^^ 3 ^ ^^^ • ^ ^* )>eriw«rcv c( %e. "^y^Cjon 

^(tc) iS Id c 5 *»»€.. "Hve SM^vi ©{ ^ J>«3jUv> Us 
COATPiTfOKCn::) "S. («^^) 15 fe ^ Oj i'»e. IKe ^um •{ 



e sn 



ARCK-R18S 



<?36 



*j?os^t"tl>,^ uPs. motst - tkjit of %t v^^cjlattt df l^e negative ^'c^*^^ 

Ire d\T€c\\v <^^f2f^ ^*^ i^i±^^ • f5wX tlie <rr«imar€6 tC 

1*1 (jo^ Ore r^viWiiAuiJc'Ay 





w 



r^^ Jer^nce cf fKe -feci] 

led o^^.iv4 0^3 

cf cj^aui^Cj- of (tie. 
Ud In Ck) ivfi^^ili^ 
c^ . , ^ ■ 

-R'^fiie resvi^CaHt <,f fa\ o>i^,af (ji.) 

T l^e '» ** Tarok^vi »♦ •* ** 

T-; - - " i^c\U * 



^ 377 ARCH- RIBS ggy 

!il»)| anQlt7€> af\d Aact] -form 1he Coviajljor.s whicti 1/^fn 7vi<**s1 -{ui- 

(I.) T-tT^.»„^^'R.^ <^^ (IL.) Ue>««lWt 
C^ T axa T rrNM-sl act in ^ke 5flt»T»< xrevtcol 0.6 «^ . 

ca% te tins S tVuJti if tV>e y«TU«alj ^ wKUk T Ah4 T 4fli ^r€ 

i2ontai Warn (^ 3€e |<«<£ o{ Fic>\H*17^ Votst ^^vj^r-e j vesuvid on 
\)erS V? "Those veYUtals tKevt T ^v^ T av£ lKe Tr€sWcTn>t r€^ 
QCUOi^S ^^^"^^ V*'*"^^ , -^v vvi)) n6«» W« . sVio%^»w lihot tKe. vevltcab 

^\ -j^ni 5 and ^fltt l)otVi fl\€ Tfertua} a*^ lKe rwa4n\tUcle<^ 
1><AM<> ^\V«vwti5(? \n<de^ evident ^ 'V^i^^r^ 4e]reirrHme<i wU'k ^~ 

c'Ail'^' x\\ <xAMix>r^te^ For t| "V lae sKifteflL cd? crr^dcvwn . «l't 

l^eui^^ sKif ^s<i aioKa Itrtir v<irlvc3t^<io kJ, t)>avcj€ ^ju vol tie } 

>'<s>W€ «f T'^^ n«r 1tve vtf^cil c^ T. T^ v<xl«4e of Y^Vu»Mrfre»-, 
r» ^x>^«^*<>iiaX to vf^» ShWloAitf -m %e -sKi {fei ^ ui, <n-d«*un^ 

tf| ouciJCHi^^rtrvvams me. same, *f U M.i^<»ffecfccl »"k e»H>^ w»aj Vy 

iKe loc^tti^ ^ ixm^ We>v»^ *\^ih*c««^ as follow^ 
yn^an^ cf § 376 

♦w^ Ki'cil va3ues of T a-,*AT'(c<:»|\ ^em T^^ a«cI T^ 3 

3 ^ B\ rtie '(♦cttovT «rf the kAYiiov^Wi "beccvK Co«n^\vuC^ oV 
Co^^JJt4(: H»t >n<C valu.eS cff T cv»^ T ^ <»kJ JKett cl^\<?yT«fHe tt»e 



§377 



ARCK-R\SS 



ss-^ 






BxamJiU ofHui . Fi^^^- 



r. 




^ 



a\ To 1^€Vvt^ of 
awd Jom '^^^ . Ti^ytv*^ he. Sum T^^ 



T^.sjpectively we deteyt-rmtc V ow^^l m ^ uC. fee i*We l/iVi 

i^vn^ cle J r «1 au VT o r« fn e vty i «cjt I ord I'^j ate 5 iVi Vev< ej>tifcl ^« lw«^*H 
Wlr^. ^Yicl aiv-eti Jjomi*S on ^ifi |>cviV>«l€V of <x )3dlv/<50h or 



3'?§- Ci-ASS^FiCATIOiM Of APCK-81BS, orFX-AS- 

T'C AK CK lb S ^ czc^oy-im^ to ConWutu/ cnn4 monies c>f Sa{»bod"t, 
In \hQ <KCc^vi*(>aTryii^ ^^iyu»€S iKe ^J^ Curves 5tt<?M/ t^g un- 
5lyam_€'<i {dTV>^ o^ JWe t\\> ^\he^0»r^ any looitJ 'Cv^vc ilj owv» w€iql»i 
19 \?tYm^tterl to convr ^on £ • ik^ iritteA <iujrve sK<jw^ <U sU*^ 
^udV* -tXo^eroiWj wW<^ W«arr»%^ a looi^, fioir-CL^sp^^vi, load** J 

Class a. ConttiXLOotS fiL^^tfC U sYij^loIerally on Ifie 

ccw^c^fc^orion v/ti' w token *4 «f^^ tu« dfti«vs, V y^'^^^K .^*t 

eal^ ju*l asif it w«y€ «i ^^'i^hi Irmz/yi^^^O "^ ^ -S-^ 

GLAS5 B.RfL^THRESKm^es^ H^r^J^o 

at the CTowv;^. F.V. 36 ^^ ou. cxomVl^ of \K>ij. >*— ^ ^^ 
TKal IS, the rii) ts dihcov^\mux.uS dttU ^ 1/^*^'rT\t 

%t nicfvit»nt <j( Hi^ sTrc^i 63u.^]€ mu,st 

tne piers 5^ Ht^ V»k c^nTf>nujOuS^€tvu€en.^ *Tk(? ktcy^ <Xr* «ovt* 
slcWe^a lm»v^c»v-alol€^ iVe. Hie sj>aw Ci;cKVxi>t cUav*^ fc a^tsi€6k%* 

sc^Hevi<< cf loodfVi^. It ts also covysUe^Y^d il^ii^e Vil i:i 

M^vultv Ho covtsfmiVit finswi tiie ]pt«TS (us "if it Vy ficxlcn 
tt>e (^TtJctHclJ not even ^U c3w/v\ weijkt ^c^Vo ]3«yiv,^tl<,i t^ 



% 378 ARCH-R^BS a30 

TW -nk- l>©rii )Dy 'ifeAdoiim^^mcUii^nC' Vb own w«i^}^^«%»44j 
"bj <x cV^^x^ije <j| "Wm^ertdtoe* Stresses di*^ 1o temjxrafcure 

_^ \ !' Con«<we frte ddiW (turve HWm dkxd( 

■«fini , ♦ ^ * - — ^ Y< 

/|.''« 4 — • -OsJ\l '^^ »i€ CcmfJi'u^ouS cunrt ^form Wfeye 

ment Y«l4w^j t« ^8j|*«^ ^ H Wynt Mow iKe ^3 

W»5 itni!:!£!^2^ ^n^ (3^^ W)^; 08 ^ ue. Ike X H^ 

....e ^f>... § 373) Jf«{-M3a.-El]- .M 

*%i 6\kty IWo Aye tUot % trtust >A^S iW*"* O ^.M) 

CLASS D. K^l^^f FiXtD EMOS Cv«i l|o\t^€S; 

Wc^e pUi€S irvK^cK <xtt IwAteil U tkc )>;€-rs . [T Kc St. Lduis 
^•5' ^^^ IniKiS class IVeva VeJna no V«n<i€i v/« liavf 
Wtum W^^yr? mM*l "jjass. However^ 5mc€ O's ^,si4Ace»M^l 



S ?78 



ARCH- R! 86 



X3f 



Wli A^ oiu,3l A^ [see ^ 373 j=: ^^YO ^ AUo^ikc W^fnt- 

V ■ '>^'i^'^*^"^''^'\ €4 \n Acre Aic n , jVt^ otvti^le Ij^^wfevi 

' ■/ '' \p I '^S^Cf t^^*>^ t^ rt^s :^«aw€ M«>4i^ Wi- 

OS w^evv ilie f\\t Vv<;ts first |>la£ 

K^nrc lie Cr)r^<iiM>n5 ^wv Wiitt^fl- \ht *}?«- 
eia{ tJ^vMlvbTium ^cl>^^on are vp 



0'. 



In \n€ 4»5*^ve me >ryva^>u:iry -n^J yroUvv5^:aHH'is at ^6 en<is 
arc s'i^owT\ r ^^^ § 3661 

37f.^ARCK R\6 KirsfO^K AT THE ENDS . U 

wMn two \m^s^X.<>cat*«n «f ^ fecial t^litrHArr, yA^- 
6| E Uxsu^uy E is the Soirne ik^D^V^K^fj |ft<»vL ft l& <5v.*eccYved 

F<'^ <ct^ V*****^ '^ ^ ^. >«^ curve v</e 
Twu»€ «n "X A**jJ 



the ^ptc/e^. >ol, Aw4 H-ve aXiS 31 (v^ieU U 06} 

t*^*^ W Vt^nsjftTrme^i CCS -fD^l^wS^Y^m^rv^Taevt^o I ^ 36 7 ^9iJ->\ 




F»5,^a^¥ 



% ST'f 



ARCH-RiBS 



^^2 







d O O 

In y^A^ital gra)f>Wcs we can ndt c^eal vvim mfrntl^^imal s 5 Wet 
we mu5it SuiksiiUite Zl^S ^ s*y\^\ Imite y©»V<»n df l>»e '^iIj^covw^ 
{<»r <Js . e^J. CO now >*<uis ^^ ^^^ As = ^^ yz As 

o o 

B4Jf we Ue AUTHE As's EQUAl., As is * ca^vv- 

Vhow "facToY Vinci CiKnCtis out ^IcAwmJ otS «-fin«ii "forvm |oy fi^ (j) 

t^p^^^f^^')--' CO' 

The cjnev twd coniitton^ ocrt ikoi ike ^>«C ,€^, V«l. '\)e9'iis *t 

jyETAlL OF THE CO/fSTRVCTiO//. 6«^e^ Ike cii!. 

l^Ke curve inVo €i'<^U / Ax> 
e^uAl As ^5 <xv»<j( "^'Z * 



tp 
» 1^ 



^V.c 



'^\K 



'P P ^iiC. <Hna w'ltt th€t^ 

tcryr\ (KAoeudi [ine AC ««> 
^•mt canvcntent 6ctxie , Wttk 







P«j. '^Si' 



%37? 



Al^CH- RUB'S 



2 33 



37^ ol. We Wow^-tK^L 08 )$iWe '^J»--Wntv^me tff Hic v€ 
"pole distance , \fj e^wxtvcw 0^ j^-^s;^ gwen^vu,. ^ tjcj .= J cjr' 

first W § 376' -fiad 1i\C v^ttc 4 l^e Summolicm ^^ ^ (ucT) 







u>tri4 fti< Sftme ))ol« «i'sT<ilnfeH 
a* fr» F>g.'^56,wt •fine! 

« . t '« " ^ U 7 " 

->» • -'a i? -'3 3 -'^ V ^ ^ 

w\\ick from %^jWff*Sr^\^\^ 
v>it obtain {vorvi F»9/^2^ 



^iS'fied ana ^t Wc iislartd^ flff <?Mjr IVicJ |?oi^^(?n infl^, 
4-C^S.j is also iVicit o| H>c $[>«cW "jjolv^ymi Sdu^itj i\e« 1^€ 

(jf COttTSC we a© not ^trvd iHoi V -vl<'* ^ 51'k . KeJac-e fte 

tb btco\>t€. €{J^u.al to ftvC. ^' 5 . That i^ ^ ttr^, 

<|u.iliWiw-rn "^^N-^oi^s rjoT tVi€ Sciir« lo«A^) ore inv€YSelv*^'itiie»v 
FoT TlS uin \ly See ^ 367> ^*^ »t iS »o T?e rerv7«vvaWv- 

ec\ Vhctt tke stresses at> iK^^ ^o*4.«n<i in tke d^ffey-^wt |)avts 

bmed mcrS€ >csuitj^i3 frorvv cKotH^c of "^et>^)>^r<a.{jixy€ ^ndl t)^e 
%\r^or)^v\\\^q of the vib oi^tS i«*e h> tV»e hn^^tvilUi] tWi^sfe 

3S0.ARCH R\6- 0F FIXED ENOS c..^^r^ch\^y 
es. EXAMPLE OF CLASS 33. As Wj^ E o^^ TaK 

Conslcint cxloKq rti€ Vi\>. Ttevs »mm<7va'b>e , Rib curve %^>m - 
ivielvieal cj^ou-t xx vcrTical line, fi«?- ^^1 sU«w^ ^ck 
OL v<\> ixvxdcr <?iny loading. Its s|5a*i is 8,wkiA is Wken 

Cufve art X <xrvcl y av\i -z. h tK€ vcvTical mWcej^t be- 



|3tyo 



ARCH- 81 BS 



236 



hew 




l(nown ^)yUi Vc W CoKi^rw^ted) "Prof. £^iyfs mettiod will 

'k>€ ai\/«v^ -^or ^wx^tUa lire 

(h^ I cure COVtster»»t 

Am^ 1W; >!=:=. H^ 

{ 2:^3^05 I XZCI5 Si 5 ^^ I y^*^^ ^ ^ -^.O^) 

«fS. (il) J 2<iS:=0 o-^J XzdS=:0 

>rL wnim -z iS Rie vertical dtstKv^e «f a^V Jvj^t ?rt'' frotvt 

/^B Ah 



i^ssssfsi. 



%390 ARCH-l^lBS • 2^G 

• — ~ ^ . — I 

\<oXc a. TVxmDcr erf ^rtncJ) £QUAL A5^S avi<i d^xcwn ct wFrliCui 

(s^€ ec^.s (23 •, tKe iXs cattCfH out "V oin4 Ae^ l^cocTs jte 
i^ecial e^U 1>ol>^<^o»'^ _j Wfrt^ vm aft<x reference-line^ l^ 



' O^ ' 



Coirv^AicwS (7; 01*4 C^^J-^na^ W sa1i^/ied b^ An -itflinnfe tiuM- 
lpeY of |:?o\^(^onS 4r^oiwvv T» I1i€ a\u€i« looAn^, Aa>J one of ItVeSc 
b€tM<> <Jrawn a** a Yyi*^ l^^^^^^*'^? "^^ <i^€n>^m€ Tor 'tt IRe 

LKvff. It must W \jjrAers\Qod ttvoi H^t ^ocant»lie5 Qm^s) %^ 

5ce FiO ^ll^J I( tV^Se Sums ctre net e^al^ ike ]x>W^»s>- 

ei' v^io (^ovw^ lViu.« ekfluvoe the z'* 's . «n H^e m*5vse -«i\io^ 

r)^cz'>S<jir\^ tb fruai«<_- tti^iSC Sujrrv? e^^u^ c»nd ^hS Satisl^ 

S5«!. DBTAlL OF COhSTRUCriO^ o\ Wt jv*,,^ 

A.f«ciM=iiB 0F Fixed ewds. dZs «« «a,4W uw «l 

^jxsn of Wit St ivOtxifc Brtdt^e wHk \^t \ta.A. tave\ri»«<i tt»g 

"Wal{ «^n or» l^e le'ft. Fi<7. ^30 , wUtre \V»6 werticej s<«le 



% 36 



Arch- RIBS 



237 



• -p -p p -p ^^ e,i,U «iu^ As'i. 

( I'i'l' 



P Ac, ^>e rkeloA^^ 







fiVst \o locale 'Z^t tv; ec||5, C6.)l f^*^ s^mmetyy U tv.ust b^ 
Waor-vlal.*Braw <x \via'\ uii^ (not showw i^x me |^uie)av\di5 ^ht 
(3-z')'^S eXC€fi li^e (-4')^5 "bs^ c^n oirrvount s:^ ^t^vC We V7n 

line ' V*'*-Tn"^ 5oa$ to v^^e ^^(z»V*'):-0 Av,4 2W'*)*:a 
\r\via i;'*^'m'*' into CL KoYi2ov>)a.] ^o5ition ftiwvs: (iVsl cJieVermiue' 



§3%l 



ARCH'R\6. FlXh)3*E\i 



XS^ 



ta«S a. heu« ^o\q oy\ akoyt^or-ilal 



tKrouxjK n^*\y^J^l^ ttie SqmeH!,'^ 



wouli "be Vonxontal , "We n-n'c^Vi (: a\5 o f>kift Itiis newlrici] j?'ol- 
\/qon. c<b wards *5floiS To Ywoi^t l^'^o-vi'*' ay^d 'l/Tn co^t^^ci'de, 

;j^"^ 's <^ Hie ftrsL VioJ ]>o'l^gi5u;^'Wu to Sol'i^f^ Coi^it.(?) 

tt iviM.^ Inav/e \ls :::^*** ^s altered |Vw <\ ce>4<?ui^ ratio jVuItUU 

i\l to tke r^^jpeclujd :z:'^'s of tke YC<^u4Yedi 5J>«cJa3 Jyo\\j(^on. 

The. next sr4> i^ te -find in wKat YaJio fke Qz'''j'S nec^ Tc 
!)€ cjJ'«rfcfll Qrr H^'* cxlVeYai m (r\>fe\rS€ yai\'oJ in ar<^ey % Id<- 
Come iVic (jz.^'/ S ', we, ivi orJev ^0 -fu^lffl Condiboh (^?^ vh» 

CiSC^' as foY I^e -r'^lo wMk. Iwo lHmi^€"5^ 

Sec R^. 4-31 ^cv ^ V-^^^ 

, J V o 



one p)-^ - 




I 



[Ti^e var>»e. Vole distance H iS i^T ^ i -^' '^ i i^ • 

' t«^?vi ^v^ Gtu these con^i^irujcl^rts ) V U ^w i ^^ 

jf.^^S ^.Ck^-^\^^-^H^l< ^^li>n (5) IS satisfied ^ live 
^jecval eijwL^dl>^^oK <jC f;^. *yL3o vutTl- Ve 

^ ^ -i^* H"' l\r?tl tills Ue ^x^a^^ct a.U 

the re^ir€^ s^«cial )>cYy5onj^ ^^a ftisloHiv mav^ i.e drau^n 
\^ Ve^lnnmg .at the, J^Vit E ^m Z/^l ^ <*r»d tK>o.:^k l^- ^v^w^ 
oe Se<Jrv,ewt U lb ike ^o|>eir >-att^ (jf ft^ ^crre diagram. Tn ^n^y 
}r^zr&. ^tgt^e (4-3^)3 ^,^ '^l^ro^^ t^aj" ..rtn^a be «»€ T^vj joth- 
l-^^ ^€ >5k ^vvdi flne ^'or^t tff t>,€4n>j a| T o^d ? W-.l^e.!^- 
line, H«v.K^ lKi5 One S€cj>Ment e{ tKe s^j^ciq] Voljtjon ^kd <jfJt- 

ht -nb ,b^ § 367. To th€ sW^sses corMtj^t^a -jroi^. "H^ese^ 

Hxr^Sp^ Q(Oyv.^l1ltf ViL, Tkesr-'^t^w^eWure stresses *\ ^d sItc;^'.- 



"fxsvcii'rm^'K 



% 3-5^ 



Al?CK-Rm5 



?4^ 



3n STi^eSS T3)AGRAMS,Tc<k. atT^^j^^Tj^ 

<^v4a^ Ms force a^'o^^um >K*ve Veen av«vun[ § 3S {] J{ ,s i-^^'uuy- 

{cy anv^ SecW of ttie^Vil ^v^T. ht. ittrusLy^^^ar ,iW mom. of 5&'eiS- 

J"j^ at c^u h<}}\itm 
of il^e -yi^ c< sec- 
iKm 15 rriouie then 



Cii^t^U, 



I 5 5 co*t^W,i 




-Ctza. tnlc iK>-efc 
sets (F;^.-'^3a) 







T=i shear 

i^3^€ %§;^?6- a>^ S673 

5ee that ihe veytwra^ l»^^€vcebt^ 
fc>€iwe«n tke r»\> civt^ rt^e -sj^^ciar 

Atoned 16 W ]>n»di<«h H Z 

Wnsjorm a Moment O/A - 



.^(itA<^ h€v»c* liie variaiiaiacf 



§ ^n ARCH^RISS S4^/ 



jl^f aA\9 «i .the SeciimT ^ 4Wvn sectiflq tb $«ct«j« a]<wj[ t^C= V»V>. 

"B\| ^rrxwtn^ a X»^*4^**%1 a*U rvx>rtvial at oinj "J^oinfc m of li»6 
^N'tJ oix'is i^ce Fi'j, ^331 «Hi "j^rtfj-ectiii^ c<ik^H ikewvi^m ti^n, 

erf h ^Slj »A/^ cWUth iKe voWeS er[ ikc frrutst (^>^d. ^Uar 

"ber ^ founts alevui tKe ^t t^-eiV voLces ma^ 1?^ W4 cr[f 
CVS \>^\tcd 1)nes j^rotM. a VtoTtjovJal cutis ^\i| rhe vcrReiJs c»h ~ 

\Yi Fi<^, '^3"^ ^ notice "^vi vA<y€ fte m.tfm^^t iS. Amavj- 
Tvum cr rv\inv\»iumr }fie ^ear-^osses mroui^V. Ti\e value 
:::r-e>o (j*^ H^^ ^ ^-^'^ .^ el#i<fv ^vtf»^^*ua)l w or- suAcl£>4w^.3c ^ 
Cardivvj A5 H^e TVxotY^, flFV- tr>oir. OCCURS l:?cTwAerL )wo '\oa^ 

Also "ib i^ ev«<^€rit (ri>j^ ^^6 <jeojH^caJ retaHei^s mvalv 
'cd ^ tW. at ttvc^ ^«5.nfe 4^ IW Vil wiitX! liva Wc^f»^t4ir»e 
t> y<KT<x\\i\ to tilt Vfjm^vtt ef rt>6 e«ju^li^d1v5«5<^ ftcst VeW 
or oiove^ Ike tWrUlt U a yv^^> t »#*vw^^ ^ \^cxjX w^^wirvx*^*^^^ 

froi^ rti€ irKJm^t Hz. 5: >a I ^ > ^^ ,H^ ^ 

e 1 ^ 

its »vxiuc, VAUfi^wK<2ycv€y ,fc occctv lit. Hie >ibi^'Vwud. k^ vvi<acl^ 



5 3B3 



ARCK-RiSS 



^^^ 



:^ arcVt-Tii^S^ fKere arc no '^KcS'>es incuitd- V^ cVi<xvi<:^e c\ If^n 
pcYaiuire j "for tHc 'forrv) 5l th€ bear*! or TruS^j H u>^^v n(? r*:^*? - 



>»«tait4r€ S . sP-^^*?"^ Called Ver-.j:?^ratuure ^Iv^s^e^ ch-e w^dutt'c? 
Nvv t-he ri? wKer; ?v«v iVi^ tsrv.}5fy atu.ir^ t" ^ IS not v^^ s^m-fc'- 

Co rv^ b } ned alt^ e brcu ^ a)^_y ^ v^th t}i ose du c to the laoA m(| 

\(x\t'^ as . ifc-i ^ STT' 
Let t = t€>**|:'n-^ 

peyoTure i 'Jii ^ ^ v. ~ 



''■».^.Cc 



(rttaZrriim^ 




On Oi'*^C 



orhan*»f"on o{ Ihe rvialH^ia.) ej[ ^Ke curved *o<»am or Vih r^ft" 
■'»n5<(iirr the acUuXi -foyrv^ 8 c^s Kavivi^ re5u}Vt?ci jVo^v. Utt 



i.-^U of 3hg^$e<}r>Tgvxt OKly ^v^2, OB. Its jone <i*ax>>«*w.'. c^^A- 
v.Vi£ 4 c< s;^<jk -ra.\j q -n* ^ see F»a. ^3^- , N^csv (^ 3"'' 3^: 

-•^^^--jj Muds^ ctwalVUHz r:: in rti.S case Hv.| 


^B ^kt^c^ for c^>4'^n;cS^^,wA 

Ift-t")??^ vTI (y'^<isiV EQUAL As 's , we 
EIl(i4;)y ^ H As Ij^ 



(^) 



InU ^rcwv el:^t t^ twenty "P^M-a^ \>a^rh C^cfU Ccillecl A S . 

1^ exfjr<!ssei^ vn. ^-IjS. ^er s<juaYe xncK ^ al) linear c^uaw1{h<< 
Sh.^u^a W »M. incV^es and H wAl W otWnSd ui ]?ounA5 . 

CW2 the JD»ojed'ton5 <f( H ufi- of O '^'' ^cpon H»e t'«tH<j«»at ^>r<> 
nc^rrAcci . Tne str«S5cs ^ue ^6 tr7ese »vvc»%/ tV»<n. "We ^etevrM^^ifcii ;v{. 

w.tH fixed EK'DS. Sef h,^. ■if 3 5', 3a.>,? I^oitu-W;. 



§3^5' 



-4~ 



!2^''r 



H .- 



^eaebed Its aetlcol 'Tc^rrrt F 

''-^. O'B.to the aJ^ <...|-,-,-.f^ 





sK^ir TRY 

p. 



Ave To be mS S<:Trvie^uvvitr Cavi^fyc^jAc a-S Wfore^^ ft>e fwo "jinceS 

the '^^O.in 8, Tc ^»n4 H <3irvd c? we 'netd t\^/a eot-uxtifjti^ 
Fvorw % 37 3 we >tAuc sUce M = H *z: ~ H C^— d. ) . 



As's 



^ Ell 



C!^-tJy=HAsj^l'/-c^ly 






;^l5(3^ :?vrnte there \xcls bee^T no cKa^tfe in rK 
tw^-lAviAhC-nls «^e must Ina-rf from ^37 






.vi^hC-nis ^ 



from § 37^ 



s=-c 



3 o 

dett^i-^MHc c:?^^^*^^ T/iCK from (33 ^^r%, <LoYv^\>iJe: H . l}v-i*w 
n,\^ the tKyusL Ov^ 5hf(>y c^ve It^f "^raj ^^^H^")^^ of V\ z O 'n'^ 






§3^5 Arch- RvbS k% 



fbr example, \\-x cr^e sjwn^^sf 55'0 f«ct^e-( tU St » 
XouiS 'B'»i^q;e ^"Kavrvv^ o^^ 'ri"5€ of 55' |€et a\^4 ^ik^i ^ilit 
e.ni^^ fn€ {aTc<? H of F<i . ^36* i$ =: lO^" ton6 wKen [{^e 
IVrv^VeraLiYe i^ So " Fakr. "KJjlicv HiaKu tlie Itwt jj. c^ erec- 
tion ^ d»^4 H7€ evtforcfd sjjav*. »«» 3 "T niclie^ SboTr^^v f^Oiit 

ture, l^vi<3e>ntl<|^ >Y "the oteJlAal ^eTvtJE>«v^atu.«r€ \ iS l^vuev- ISa^-i 

Aval <7f" fi^^, ^35 and V3Y, 

, 3%6. STRESSES 5;}UET0 KtS-SHCRTENlNi'Q. 

^il-pvii^jl^ A' S ^ ^<4.e to Vne Hn»^n4v <3h4YjWe<i IVirust "b, F. 

^OTfH jy^ %Q lnl> ogci^ . THi6 cVj«xv»j€ m me W^Hi ^f th-^ di^'fcf- 
«*vit ^oyPtonS <sf \Vie y»\> curve rno-V oe tVeoled as^f ?t wevei^^ 

See th^ a. {liTiAst ejf tfO 1o»i« Cdrvt\»Tl 'u|>ch ^ secUcH^ia- 
«<X or F ^ IQ S<>,iifc\>e5 th <»>^ «^^" rw ^w/hcrs€ 'rt-aliena^} 

di>«e to a (cus cf ]'ctM.^frctluY (2 (^t ~tj Jevlvc(i as fo/'^*?; 

f^txKr«irvWe»C T ur-.i^ men av^ ^^'^*\ 

PracUcaily ttien s1k»c6 tr^ost nr»eta2 ccrcW tni^jc^ o] C!^:^^- 
£S C cvwi "i) Ore ralKev flat »u cw<YvAr«At e ^ c^vid ihe ^n^oiSi, 
^4 T«> o>-<i^v*ary rviodlt'S of )oa<l »\i/j 4»<'5 ^'^^'^ vavy vv,ore ikcikt 

50 £?>- 30 f^ercent. al©n<i It?6 ^»b ^ ^w \'m<^'?»'nayy fall ef 



in^ a'b (lie evi4^ <\re hlnje^ ^^r f'Xe<J^^ |rovvN w/Klcla new Imusa 
3\\tars <^n<i •itrc^S'^coM^W Yv»omev»t^^1rn^v| be deyivea To he 

3S 7. R^5UME . It i-s adw sc<;»i >i«w Ike s1y€S5cs \tY 

i-v\£\»j he. c»\>taiv\( 

«\rek-'r»lo ov c«Arve3i Vcarw of ike 'l<i\Aa4 <At5CYtl>e<^ ^ b^^ ccw- 

l^invn^ tKe ve5uAt6 <J.k€ to Hie iKrct se^^\afe ^•a^SeS^viV. ; 

CAM^ecl ^ l1i£ tkru^t"^ due to t^i6 \oacl» ^Thal i*5, tn <^»jy e^^^s^^' 



vied \n aJV Jxrrti of tun^ seetiin <jf a ^Aii 



-F 






..(0 
F I ' 

^^ f^"<3 ^ V3 6 sKovwS tlTe ryy e(^y\\y}cj « J C 

^ rihe S<^m^ ^'>^^ "Vityefo-^or^J X <^ 
'\ \^t rvOlv^enl of \n^Yt»cc ef ^t i^c- 

I'V ^o^-ifal^ C. F- cx^eo. <^ Cross -SfC- 

r- ^ ^ ^ J •• "^ /^ > 

h>e iv\ciy«iMwuy\ sly ess ni. oi <:^lw^vt 
y\h J or de$?<)n tKe Vilo 50 )1^at Tl^is 
IwoL^imutvL styeSS ^Wa}l l^c '=>a{e for Iffe 

>5 cVtaiWed fcv ^wy section Tc coivtjow/T^ ck •bTx>f>tr 




/3G 



% 3S1. 



ARCH-f^lBS 



^^7 



?h 



iik^neiS af w-tljj s|x>.ftna '«f rivets, ttc. 

387. THE AftCH-TRUSS,or V 



V rteai"^ aS o \>€am «rf co>^t<^"^^ Section c\^^iyu>fWTfit ci[ 
tr^t C obi en 15 S-riJcje T^^^ § ^*^ C]ass T) j TnAy bt htot- 

i^tTt". of tlie "^Jieces I! tc tiie CvtrvedL 
T>"*?<^n| rtiiS curve<i axis 

ife ^ei-ce dLia^T?:im for i^ro-tK 1< 
ir\q. A^y |?Uf.<. I" to 4e Vit Axi5 
i>»^<rt \t crcjsses lVic 



1 



"J>Hrr 







fo Vme "^0}^^^ 



"J>vO>vt 



,;-^//.-y." 



tkv..st -- T. 



^ 
A^^ 






S 3^7 



AkXM- ^IBS 



?^-^8 






^1 



us St< 



r? if a 



covinbr ess foil 



crv.ci rnmwS c{ tevi^ ^o n^ d%^ /-^ /^ P''^^ =r H 21 ..,(3) 



^- 






<<?»r* 



HoRizgivtAK "Straight QlRi^^^^RS: 



Voce 



thai tkere U no VsY^^^ou^re \o KcrrJovttJ. 7vu?ti^,fVa.^3f 



V -1 



Y=7,'3 




i n 



}y tent 

V<iirricc»1 

^^•^ jn tWvs case 
Vi^V^rt hi? n.<yrT-2or>fal eon&tVavnt Ja.5 a, V^-rliC^o^t- cast 
0] tf.vi aj-cU T^k^'ft J^ evJc^ent W^d since "H-\^ )>ol< a^Wcf 

u[ -no rndnnfcrttj -Tre-sjitctWclv .^ but !:ei\-<^ vertical vuMl tjoI; in- 



II I ., 1^ — —^ — ~ — «* — ' ^ ■ »... .., , . L 

<J7au A5. ^i^:^ue tke^cliuxl sj?ec. <cjct.l(» |>o]/i^ useless . 
Section m (t"Vc{»^5^)wK%c>i wt wisit To ciereTn\t>ie^K»«tilfnt*e 



t^ TIC lViTu.st oloi^ tVt^ oeam^ fiind l<KOwivii>- "taotton nv;g(,4<vi arvij^ 



{oK€ H *^)l>^»edL Kcmz&wAxfly at ecxch evid ^ me W<7!m x^Jiii. 

;>^vvCt: the shears c^ncl n\Dmfnts tv»A^ W ^H^Kie^ <rr<x{>Vi<;<:5V)y 
acT»oi^s V ^av^a ^ J «\H^ ijie tvu6 ^quxkX ou.d oi^5^^e H*^^, 

v«yr JrGvity oix»5 K ere) of rr tne naornef^t ^t -m wUl W wv^a^^ 

Reeled hyj '\l *j av^ 5ivic£ W^ W^ ^^ cet^^dnevrt F" tc .^e 

'bearv. cxtr m ^ in 6 sKcx^*^ ^^ Trt j^ me saivic \vi ^e v^i?Mr 

s^^5\<?^K o| '[<rrctfs^ ojs m IV\e o1<l-b«f ore TKe vnfVo^-u^rtiori ijf 

■me H'"s.3 

Hcnre Wm of{ Hie loaJ-lme. h, ?♦.. S Fv^ .^3?^ ^ndi con- 
struct c?iv\ d<>uil, *bo\yo. v/KicW sK«ll T?flC^ frirot^^n A '^^^'^ 

O' (ocr'o<Wciyy^^an<i Growing OS' 4 tb A' 5'. Txl<u'»^| O" 
Trie tvioiMCvil e-^ intTfi(i fC?ed net f»e ca»A5lG„<^ ',n Hiit. Ca.*e, 



> 3 b' f A^^ CH - K 1 B 5 ; mc ihi c/\s .^ ^ $rt?Atci NT !< $ 

Saine 5evel^ We YnAu consiaeY The VvMeb^aivi. 4ret.(cH*^iHa cicsC 

I m Til 6 u>%KMew.'rt 
uj^wav^ sheave 




ts 






sections, A% 



^ S^^cts in 



3S^ 



P / »yCn Vkowtv vorUccd tii^t 



W2 have 2" Mx.A-S:=: o •; 5 H'zxAs^c o v; ^xtlA^^g 
^...;ct W EaUAL Zls s ^ S C^)- O ana X(xz.) ==^0(^377) 
N<^w Y^ Okrt^ Me C"" dY-aw o^y^ e^4*^lvpeJ, F*^ C *** <^^ m !w)sx:a^£ 

/ ' to ^ix '^". T^e ci pole O** cK Ihe Kav^z. 1\irf>' Ti*^?^^^ 

tvcj^ iHtS jjol, FG *^^^ ^C aMn<*^€ci H-ie r>rowi«.^ ^W^ skeco-j jyror*< 



^rov if ^ 



